/*
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 * 
 *  Some functions in this file use the VSOP87 solution by
 *  Messrs. Bretagnon and Francou.
 * 
 *  Copyright (C) 2000 - 2005 Liam Girdwood  
 */

#include <math.h>
#include <libnova/mars.h>
#include <libnova/vsop87.h>
#include <libnova/solar.h>
#include <libnova/earth.h>
#include <libnova/transform.h>
#include <libnova/rise_set.h>
#include <libnova/utility.h>

#define LONG_L0 1409
#define LONG_L1 891
#define LONG_L2 442
#define LONG_L3 194
#define LONG_L4 75
#define LONG_L5 24
#define LAT_B0 441
#define LAT_B1 291
#define LAT_B2 161
#define LAT_B3 64
#define LAT_B4 18
#define LAT_B5 9
#define RADIUS_R0 1107
#define RADIUS_R1 672
#define RADIUS_R2 368
#define RADIUS_R3 160
#define RADIUS_R4 57
#define RADIUS_R5 17

/* cache variables */
static double cJD = 0, cL = 0, cB = 0, cR = 0;


static const struct ln_vsop mars_longitude_l0[LONG_L0] = {
    {     6.20347711581,  0.00000000000,        0.00000000000}, 
    {     0.18656368093,  5.05037100270,     3340.61242669980}, 
    {     0.01108216816,  5.40099836344,     6681.22485339960}, 
    {     0.00091798406,  5.75478744667,    10021.83728009940}, 
    {     0.00027744987,  5.97049513147,        3.52311834900}, 
    {     0.00010610235,  2.93958560338,     2281.23049651060}, 
    {     0.00012315897,  0.84956094002,     2810.92146160520}, 
    {     0.00008926784,  4.15697846427,        0.01725365220}, 
    {     0.00008715691,  6.11005153139,    13362.44970679920}, 
    {     0.00006797556,  0.36462229657,      398.14900340820}, 
    {     0.00007774872,  3.33968761376,     5621.84292321040}, 
    {     0.00003575078,  1.66186505710,     2544.31441988340}, 
    {     0.00004161108,  0.22814971327,     2942.46342329160}, 
    {     0.00003075252,  0.85696614132,      191.44826611160}, 
    {     0.00002628117,  0.64806124465,     3337.08930835080}, 
    {     0.00002937546,  6.07893711402,        0.06731030280}, 
    {     0.00002389414,  5.03896442664,      796.29800681640}, 
    {     0.00002579844,  0.02996736156,     3344.13554504880}, 
    {     0.00001528141,  1.14979301996,     6151.53388830500}, 
    {     0.00001798806,  0.65634057445,      529.69096509460}, 
    {     0.00001264357,  3.62275122593,     5092.15195811580}, 
    {     0.00001286228,  3.06796065034,     2146.16541647520}, 
    {     0.00001546404,  2.91579701718,     1751.53953141600}, 
    {     0.00001024902,  3.69334099279,     8962.45534991020}, 
    {     0.00000891566,  0.18293837498,    16703.06213349900}, 
    {     0.00000858759,  2.40093811940,     2914.01423582380}, 
    {     0.00000832715,  2.46418619474,     3340.59517304760}, 
    {     0.00000832720,  4.49495782139,     3340.62968035200}, 
    {     0.00000712902,  3.66335473479,     1059.38193018920}, 
    {     0.00000748723,  3.82248614017,      155.42039943420}, 
    {     0.00000723861,  0.67497311481,     3738.76143010800}, 
    {     0.00000635548,  2.92182225127,     8432.76438481560}, 
    {     0.00000655162,  0.48864064125,     3127.31333126180}, 
    {     0.00000550474,  3.81001042328,        0.98032106820}, 
    {     0.00000552750,  4.47479317037,     1748.01641306700}, 
    {     0.00000425966,  0.55364317304,     6283.07584999140}, 
    {     0.00000415131,  0.49662285038,      213.29909543800}, 
    {     0.00000472167,  3.62547124025,     1194.44701022460}, 
    {     0.00000306551,  0.38052848348,     6684.74797174860}, 
    {     0.00000312141,  0.99853944405,     6677.70173505060}, 
    {     0.00000293198,  4.22131299634,       20.77539549240}, 
    {     0.00000302375,  4.48618007156,     3532.06069281140}, 
    {     0.00000274027,  0.54222167059,     3340.54511639700}, 
    {     0.00000281079,  5.88163521788,     1349.86740965880}, 
    {     0.00000231183,  1.28242156993,     3870.30339179440}, 
    {     0.00000283602,  5.76885434940,     3149.16416058820}, 
    {     0.00000236117,  5.75503217933,     3333.49887969900}, 
    {     0.00000274033,  0.13372524985,     3340.67973700260}, 
    {     0.00000299395,  2.78323740866,     6254.62666252360}, 
    {     0.00000204162,  2.82133445874,     1221.84856632140}, 
    {     0.00000238866,  5.37153646326,     4136.91043351620}, 
    {     0.00000188648,  1.49104066040,     9492.14631500480}, 
    {     0.00000221228,  3.50466812198,      382.89653222320}, 
    {     0.00000179196,  1.00561962003,      951.71840625060}, 
    {     0.00000172117,  0.43943649536,     5486.77784317500}, 
    {     0.00000193118,  3.35716641911,        3.59042865180}, 
    {     0.00000144304,  1.41874112114,      135.06508003540}, 
    {     0.00000160016,  3.94857092451,     4562.46099302120}, 
    {     0.00000174072,  2.41361337725,      553.56940284240}, 
    {     0.00000130989,  4.04491134956,    12303.06777661000}, 
    {     0.00000138243,  4.30145122848,        7.11354700080}, 
    {     0.00000128062,  1.80665816220,     5088.62883976680}, 
    {     0.00000139898,  3.32595559208,     2700.71514038580}, 
    {     0.00000128105,  2.20807538189,     1592.59601363280}, 
    {     0.00000116944,  3.12806863456,     7903.07341972100}, 
    {     0.00000110378,  1.05194545948,      242.72860397400}, 
    {     0.00000113481,  3.70070432339,     1589.07289528380}, 
    {     0.00000100099,  3.24340223714,    11773.37681151540}, 
    {     0.00000095594,  0.53950648295,    20043.67456019880}, 
    {     0.00000098947,  4.84558326403,     6681.24210705180}, 
    {     0.00000104542,  0.78532737699,     8827.39026987480}, 
    {     0.00000084186,  3.98971116025,     4399.99435688900}, 
    {     0.00000086928,  2.20183965407,    11243.68584642080}, 
    {     0.00000071438,  2.80307223477,     3185.19202726560}, 
    {     0.00000072095,  5.84669532401,     5884.92684658320}, 
    {     0.00000073482,  2.18421190324,     8429.24126646660}, 
    {     0.00000098946,  2.81481171439,     6681.20759974740}, 
    {     0.00000068413,  2.73834597183,     2288.34404351140}, 
    {     0.00000086747,  1.02091867465,     7079.37385680780}, 
    {     0.00000065316,  2.68114882713,       28.44918746780}, 
    {     0.00000083745,  3.20254912006,     4690.47983635860}, 
    {     0.00000075031,  0.76647765061,     6467.92575796160}, 
    {     0.00000068983,  3.76403440528,     6041.32756708560}, 
    {     0.00000066706,  0.73630288873,     3723.50895892300}, 
    {     0.00000063313,  4.52771850220,      426.59819087600}, 
    {     0.00000061684,  6.16831461502,     2274.11694950980}, 
    {     0.00000052260,  0.89938935091,     9623.68827669120}, 
    {     0.00000055485,  4.60622447136,     4292.33083295040}, 
    {     0.00000051331,  4.14823934301,     3341.59274776800}, 
    {     0.00000056633,  5.06250402329,       15.25247118500}, 
    {     0.00000063376,  0.91293637746,     3553.91152213780}, 
    {     0.00000045822,  0.78790300125,     1990.74501704100}, 
    {     0.00000048553,  3.95677994023,     4535.05943692440}, 
    {     0.00000041223,  6.02013764154,     3894.18182954220}, 
    {     0.00000041941,  3.58309124437,     8031.09226305840}, 
    {     0.00000056395,  1.68727941626,     6872.67311951120}, 
    {     0.00000055907,  3.46261441099,      263.08392337280}, 
    {     0.00000051677,  2.81307639242,     3339.63210563160}, 
    {     0.00000040669,  3.13838566327,     9595.23908922340}, 
    {     0.00000038111,  0.73396370751,    10025.36039844840}, 
    {     0.00000039498,  5.63225741360,     3097.88382272579}, 
    {     0.00000044175,  3.19530118759,     5628.95647021120}, 
    {     0.00000036718,  2.63750919104,      692.15760122680}, 
    {     0.00000045905,  0.28717581576,     5614.72937620960}, 
    {     0.00000038351,  5.82880639987,     3191.04922956520}, 
    {     0.00000038198,  2.34832438823,      162.46663613220}, 
    {     0.00000032561,  0.48401318272,     6681.29216370240}, 
    {     0.00000037135,  0.68510839331,     2818.03500860600}, 
    {     0.00000031169,  3.98160436995,       20.35531939880}, 
    {     0.00000032561,  0.89250965753,     6681.15754309680}, 
    {     0.00000037749,  4.15481250779,     2803.80791460440}, 
    {     0.00000033626,  6.11997987693,     6489.77658728800}, 
    {     0.00000029007,  2.42707198395,     3319.83703120740}, 
    {     0.00000038794,  1.35194224244,    10018.31416175040}, 
    {     0.00000033149,  1.14024195200,        5.52292430740}, 
    {     0.00000027583,  1.59721760699,     7210.91581849420}, 
    {     0.00000028699,  5.72047550940,     7477.52286021600}, 
    {     0.00000034039,  2.59525636978,    11769.85369316640}, 
    {     0.00000025380,  0.52092092633,       10.63666534980}, 
    {     0.00000026355,  1.34519007001,     3496.03282613400}, 
    {     0.00000024555,  4.00321315879,    11371.70468975820}, 
    {     0.00000025637,  0.24963503109,      522.57741809380}, 
    {     0.00000027275,  4.55649766071,     3361.38782219220}, 
    {     0.00000023766,  1.84063759173,    12832.75874170460}, 
    {     0.00000022814,  3.52628452806,     1648.44675719740}, 
    {     0.00000022272,  0.72111173236,      266.60704172180}, 
    {     0.00000021201,  3.11823578369,     2957.71589447660}, 
    {     0.00000020156,  3.67147308710,     1758.65307841680}, 
    {     0.00000021530,  6.15388673691,     3264.34635542420}, 
    {     0.00000020090,  1.08241387913,     7064.12138562280}, 
    {     0.00000021344,  4.28178434496,     4032.77002792660}, 
    {     0.00000027541,  6.08386421472,     6674.11130639880}, 
    {     0.00000019842,  2.37674123073,    10713.99488132620}, 
    {     0.00000025518,  3.43241978555,     3443.70520091840}, 
    {     0.00000022542,  5.64861441506,     2388.89402044920}, 
    {     0.00000024376,  0.97006548518,      632.78373931320}, 
    {     0.00000023079,  4.74990771219,     3347.72597370060}, 
    {     0.00000017708,  3.69743280195,     3344.20285535160}, 
    {     0.00000022658,  3.95447568336,     4989.05918389720}, 
    {     0.00000022600,  5.24085203262,     3205.54734666440}, 
    {     0.00000016811,  5.48619684184,        3.88133535800}, 
    {     0.00000018422,  4.22550249103,     2787.04302385740}, 
    {     0.00000022735,  4.98523942294,     7632.94325965020}, 
    {     0.00000016638,  2.52822534159,    14584.29827312060}, 
    {     0.00000020963,  4.27879531719,     5099.26550511660}, 
    {     0.00000016033,  1.76789519365,     3475.67750673520}, 
    {     0.00000015814,  3.13241857680,       59.37386191360}, 
    {     0.00000018113,  3.25756742113,     3337.02199804800}, 
    {     0.00000019295,  3.23912725911,        7.04623669800}, 
    {     0.00000016777,  4.39731653353,    15643.68020330980}, 
    {     0.00000017554,  4.09198247074,       74.78159856730}, 
    {     0.00000013713,  2.54103541653,     4933.20844033260}, 
    {     0.00000016007,  1.54673981973,    14054.60730802600}, 
    {     0.00000014603,  3.45689862899,     7373.38245462640}, 
    {     0.00000013547,  4.04141743525,     4929.68532198360}, 
    {     0.00000014222,  0.59967781578,       23.87843774780}, 
    {     0.00000013876,  5.40880274251,    10973.55568635000}, 
    {     0.00000014026,  1.44210504015,    10404.73381232260}, 
    {     0.00000016055,  3.79399064336,     2118.76386037840}, 
    {     0.00000013717,  3.59037690181,    15113.98923821520}, 
    {     0.00000018040,  4.25416134565,     2487.41604494780}, 
    {     0.00000015846,  0.56902641445,      103.09277421860}, 
    {     0.00000013402,  5.16918481175,    10213.28554621100}, 
    {     0.00000016068,  2.36894092837,     3265.83082813250}, 
    {     0.00000012773,  0.10474161940,     7234.79425624200}, 
    {     0.00000012197,  1.73028863618,       36.02786667740}, 
    {     0.00000012283,  5.19941258642,    10021.85453375160}, 
    {     0.00000011947,  5.47980574430,     2921.12778282460}, 
    {     0.00000011890,  4.76587196145,     5828.02847164760}, 
    {     0.00000012283,  3.16864076359,    10021.82002644720}, 
    {     0.00000013269,  6.17851484916,     1744.42598441520}, 
    {     0.00000011749,  5.72731481869,        0.42007609361}, 
    {     0.00000012340,  2.52148348822,     2906.90068882300}, 
    {     0.00000014458,  4.38011275876,      316.39186965660}, 
    {     0.00000010640,  3.44997335322,      639.89728631400}, 
    {     0.00000010925,  0.60402475795,     5085.03841111500}, 
    {     0.00000010646,  5.47663096745,      419.48464387520}, 
    {     0.00000010795,  1.37204952026,    10419.98628350760}, 
    {     0.00000010573,  1.09027262515,    12168.00269657460}, 
    {     0.00000009578,  4.89483638811,     3230.40610548040}, 
    {     0.00000009805,  5.83614893022,    14314.16811304980}, 
    {     0.00000009718,  0.00011311901,     9225.53927328300}, 
    {     0.00000009146,  1.10288559040,     9808.53818466140}, 
    {     0.00000009779,  3.60055224203,      206.18554843720}, 
    {     0.00000012732,  1.79880344270,    13745.34623902240}, 
    {     0.00000012156,  4.42292535673,    14712.31711645800}, 
    {     0.00000008805,  3.97132756722,      170.67287061920}, 
    {     0.00000010682,  4.33907151559,     7740.60678358880}, 
    {     0.00000010040,  1.38291942087,     3583.34103067380}, 
    {     0.00000009961,  2.69116597350,       36.60536530420}, 
    {     0.00000008473,  4.29275471153,        0.42988312670}, 
    {     0.00000010584,  0.89643083679,    23384.28698689860}, 
    {     0.00000009597,  4.33289499954,      131.54196168640}, 
    {     0.00000008477,  2.86885079661,     9381.93999378540}, 
    {     0.00000008436,  3.15234316178,     6525.80445396540}, 
    {     0.00000007518,  1.24474332957,     6894.52394883760}, 
    {     0.00000006746,  1.58828730801,     6836.64525283380}, 
    {     0.00000006722,  4.38897665506,       66.48740891440}, 
    {     0.00000006738,  5.77292945138,     5202.35827933520}, 
    {     0.00000006243,  1.57847357313,     3325.35995551480}, 
    {     0.00000008446,  2.90692880268,       43.71891230500}, 
    {     0.00000006482,  6.03333628981,      574.34479833480}, 
    {     0.00000006348,  0.06986409522,     1964.83862685400}, 
    {     0.00000006193,  5.43709781754,     1861.74585263540}, 
    {     0.00000008246,  0.44145777409,     2707.82868738660}, 
    {     0.00000005987,  4.22748552841,     4459.36821880260}, 
    {     0.00000006530,  1.24945509771,    12964.30070339100}, 
    {     0.00000005949,  0.77228459543,     2699.73481931760}, 
    {     0.00000007339,  4.95735130126,     3767.21061757580}, 
    {     0.00000006135,  3.16322568315,     6680.24453233140}, 
    {     0.00000006027,  3.01298246255,     3369.06161416760}, 
    {     0.00000005857,  4.30341888951,     7875.67186362420}, 
    {     0.00000006360,  1.77803516211,     2178.13772229200}, 
    {     0.00000005771,  0.96116030741,    13916.01910964160}, 
    {     0.00000006100,  4.49881794524,     6682.20517446780}, 
    {     0.00000005777,  4.92993290350,     2384.32327072920}, 
    {     0.00000007647,  6.16291591270,     6531.66165626500}, 
    {     0.00000007242,  0.52885257496,    10575.40668294180}, 
    {     0.00000005311,  4.51564606382,     6144.42034130420}, 
    {     0.00000005212,  3.49017198482,    12935.85151592320}, 
    {     0.00000006680,  3.48192412858,     1118.75579210280}, 
    {     0.00000005226,  3.25464016223,     2391.43681773000}, 
    {     0.00000005215,  0.01031380055,      533.21408344360}, 
    {     0.00000005534,  3.42311181658,     3134.42687826260}, 
    {     0.00000005437,  6.18510783147,     8425.65083781480}, 
    {     0.00000005774,  3.55189251089,     8969.56889691100}, 
    {     0.00000005093,  0.60862188744,     8955.34180290940}, 
    {     0.00000004840,  4.63233532160,     4569.57454002200}, 
    {     0.00000005828,  5.92311700172,      640.87760738220}, 
    {     0.00000005686,  0.76212811066,     3120.19978426100}, 
    {     0.00000004912,  1.70752765226,    13358.92658845020}, 
    {     0.00000005490,  4.29423846802,     3503.07906283200}, 
    {     0.00000004676,  3.34239248969,     3116.26763099790}, 
    {     0.00000005858,  2.38460385828,     3302.47939106200}, 
    {     0.00000005098,  1.12472834482,     5331.35744374080}, 
    {     0.00000004412,  1.38574902846,    17256.63153634140}, 
    {     0.00000004261,  1.69359026235,    13524.91634293140}, 
    {     0.00000004191,  0.19115182648,     9830.38901398780}, 
    {     0.00000004164,  0.43810126153,     1066.49547719000}, 
    {     0.00000005192,  3.63498024808,      536.80451209540}, 
    {     0.00000005664,  0.50444427941,     5305.45105355380}, 
    {     0.00000005477,  5.96812391483,     3074.00538497800}, 
    {     0.00000005303,  5.40010329848,     3355.86489788480}, 
    {     0.00000004043,  0.83846792979,    10021.90459040220}, 
    {     0.00000004153,  3.14489443759,     8439.87793181640}, 
    {     0.00000004818,  1.08987352671,    13365.97282514820}, 
    {     0.00000004906,  3.73076098617,     1228.96211332220}, 
    {     0.00000004577,  0.99356399425,     6158.64743530580}, 
    {     0.00000004244,  3.87048930395,     3312.16323923200}, 
    {     0.00000004895,  6.24828800623,    17654.78053974960}, 
    {     0.00000003595,  6.07310183986,    10818.13528691580}, 
    {     0.00000003756,  1.37897245496,     3973.39616601300}, 
    {     0.00000003550,  1.87497578775,    17395.21973472580}, 
    {     0.00000004422,  2.89970459985,     6247.51311552280}, 
    {     0.00000003974,  4.03444710872,     1052.26838318840}, 
    {     0.00000003488,  4.27354225380,     3178.14579056760}, 
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    {     0.00000000037,  5.60013944614,     8123.50331581200}, 
    {     0.00000000039,  2.12359970883,    23387.81010524760}, 
    {     0.00000000037,  5.00181395644,    17810.20093918380}, 
    {     0.00000000038,  6.00950016545,     4295.85395129940}, 
    {     0.00000000040,  6.05295156557,     6151.55114195720}, 
    {     0.00000000036,  0.42674900890,     9997.95884235160}, 
    {     0.00000000044,  4.13342515647,    12192.86145539060}, 
    {     0.00000000037,  2.57249437155,     9815.13654280280}, 
    {     0.00000000036,  0.30459710615,    10618.01565410840}, 
    {     0.00000000039,  1.53352233747,     6683.97636401060}, 
    {     0.00000000050,  5.87136225569,     4396.47123854000}, 
    {     0.00000000040,  4.58209614492,     8294.17618643120}, 
    {     0.00000000036,  3.26497387820,    16269.35039562219}, 
    {     0.00000000040,  4.17543231683,     9962.46341818580}, 
    {     0.00000000036,  1.95918123970,      360.11078196160}, 
    {     0.00000000038,  2.38454082948,    24093.27678917520}, 
    {     0.00000000036,  2.85429847882,     6549.68289171320}, 
    {     0.00000000038,  3.54096291728,    19683.56377823720}, 
    {     0.00000000037,  3.74762124247,     1045.15483618760}, 
    {     0.00000000043,  5.45850357191,    17608.51883016380}, 
    {     0.00000000039,  5.88001746710,     4709.27267954480}, 
    {     0.00000000040,  4.23855320433,     3339.43178404770}, 
    {     0.00000000042,  3.73781410726,     7593.79509706520}, 
};


static const struct ln_vsop mars_longitude_l1[LONG_L1] = {
    {  3340.61242700512,  0.00000000000,        0.00000000000}, 
    {     0.01457554523,  3.60433733236,     3340.61242669980}, 
    {     0.00168414711,  3.92318567804,     6681.22485339960}, 
    {     0.00020622975,  4.26108844583,    10021.83728009940}, 
    {     0.00003452392,  4.73210393190,        3.52311834900}, 
    {     0.00002586332,  4.60670058555,    13362.44970679920}, 
    {     0.00000841535,  4.45864030426,     2281.23049651060}, 
    {     0.00000537567,  5.01581256923,      398.14900340820}, 
    {     0.00000520948,  4.99428054039,     3344.13554504880}, 
    {     0.00000432635,  2.56070853083,      191.44826611160}, 
    {     0.00000429655,  5.31645299471,      155.42039943420}, 
    {     0.00000381751,  3.53878166043,      796.29800681640}, 
    {     0.00000328530,  4.95632685192,    16703.06213349900}, 
    {     0.00000282795,  3.15966768785,     2544.31441988340}, 
    {     0.00000205657,  4.56889279932,     2146.16541647520}, 
    {     0.00000168866,  1.32936559060,     3337.08930835080}, 
    {     0.00000157593,  4.18519540728,     1751.53953141600}, 
    {     0.00000133686,  2.23327245555,        0.98032106820}, 
    {     0.00000116965,  2.21414273762,     1059.38193018920}, 
    {     0.00000117503,  6.02411290806,     6151.53388830500}, 
    {     0.00000113718,  5.42753341019,     3738.76143010800}, 
    {     0.00000133565,  5.97420357518,     1748.01641306700}, 
    {     0.00000091099,  1.09626613064,     1349.86740965880}, 
    {     0.00000084256,  5.29330740437,     6684.74797174860}, 
    {     0.00000113886,  2.12863726524,     1194.44701022460}, 
    {     0.00000080823,  4.42818326716,      529.69096509460}, 
    {     0.00000079847,  2.24822372859,     8962.45534991020}, 
    {     0.00000072505,  5.84203374239,      242.72860397400}, 
    {     0.00000072945,  2.50193599662,      951.71840625060}, 
    {     0.00000071490,  3.85645759558,     2914.01423582380}, 
    {     0.00000085340,  3.90856932983,      553.56940284240}, 
    {     0.00000067580,  5.02334895070,      382.89653222320}, 
    {     0.00000065060,  1.01810963274,     3340.59517304760}, 
    {     0.00000065061,  3.04888114328,     3340.62968035200}, 
    {     0.00000061478,  4.15185188249,     3149.16416058820}, 
    {     0.00000048482,  4.87339233007,      213.29909543800}, 
    {     0.00000046581,  1.31461442691,     3185.19202726560}, 
    {     0.00000056642,  3.88772102421,     4136.91043351620}, 
    {     0.00000047615,  1.18228660215,     3333.49887969900}, 
    {     0.00000042052,  5.30826745759,    20043.67456019880}, 
    {     0.00000041330,  0.71392238704,     1592.59601363280}, 
    {     0.00000040280,  2.72571311592,        7.11354700080}, 
    {     0.00000033040,  5.40823104809,     6283.07584999140}, 
    {     0.00000028676,  0.04305323493,     9492.14631500480}, 
    {     0.00000022322,  5.86718681699,     3870.30339179440}, 
    {     0.00000022432,  5.46596961275,       20.35531939880}, 
    {     0.00000022606,  0.83782540818,     3097.88382272579}, 
    {     0.00000021416,  5.37936489667,     3340.54511639700}, 
    {     0.00000023347,  6.16774433900,     3532.06069281140}, 
    {     0.00000026573,  3.89000631130,     1221.84856632140}, 
    {     0.00000022800,  1.54501542908,     2274.11694950980}, 
    {     0.00000020474,  2.36236861670,     1589.07289528380}, 
    {     0.00000020179,  3.36390759347,     5088.62883976680}, 
    {     0.00000020013,  2.57546546037,    12303.06777661000}, 
    {     0.00000019920,  0.44761063096,     6677.70173505060}, 
    {     0.00000026550,  5.11303525089,     2700.71514038580}, 
    {     0.00000021104,  3.52541056271,       15.25247118500}, 
    {     0.00000021424,  4.97083417225,     3340.67973700260}, 
    {     0.00000018502,  5.57854926842,     1990.74501704100}, 
    {     0.00000017805,  6.12513609945,     4292.33083295040}, 
    {     0.00000016463,  2.60307709195,     3341.59274776800}, 
    {     0.00000016592,  1.25515357212,     3894.18182954220}, 
    {     0.00000019864,  2.52765519587,     4399.99435688900}, 
    {     0.00000015002,  1.03518790208,     2288.34404351140}, 
    {     0.00000020011,  4.73112374598,     4690.47983635860}, 
    {     0.00000015431,  2.46932776517,     4535.05943692440}, 
    {     0.00000020193,  5.78561467842,     7079.37385680780}, 
    {     0.00000015298,  2.26504738206,     3723.50895892300}, 
    {     0.00000015019,  3.36690751539,     6681.24210705180}, 
    {     0.00000013219,  5.61412860968,    10025.36039844840}, 
    {     0.00000013517,  2.12392880454,     5486.77784317500}, 
    {     0.00000015019,  1.33613594479,     6681.20759974740}, 
    {     0.00000012676,  2.95036175206,     3496.03282613400}, 
    {     0.00000013644,  1.97710249337,     5614.72937620960}, 
    {     0.00000013011,  1.51458564766,     5628.95647021120}, 
    {     0.00000011353,  6.23411904718,      135.06508003540}, 
    {     0.00000013508,  3.42721826602,     5621.84292321040}, 
    {     0.00000010866,  5.28165480979,     2818.03500860600}, 
    {     0.00000011880,  3.12847055823,      426.59819087600}, 
    {     0.00000010467,  2.73598607050,     2787.04302385740}, 
    {     0.00000011131,  5.84122566289,     2803.80791460440}, 
    {     0.00000011770,  2.58277425311,     8432.76438481560}, 
    {     0.00000011861,  5.47552055459,     3553.91152213780}, 
    {     0.00000008540,  1.91739325491,    11773.37681151540}, 
    {     0.00000009819,  4.52958330672,     6489.77658728800}, 
    {     0.00000008552,  3.16147568714,      162.46663613220}, 
    {     0.00000010957,  4.15775327007,     2388.89402044920}, 
    {     0.00000008948,  4.23164385777,     7477.52286021600}, 
    {     0.00000008131,  1.61308074119,     2957.71589447660}, 
    {     0.00000008352,  2.18475645206,       23.87843774780}, 
    {     0.00000008030,  5.69889507906,     6041.32756708560}, 
    {     0.00000007878,  5.71359767892,     9623.68827669120}, 
    {     0.00000008713,  4.43300582398,     5092.15195811580}, 
    {     0.00000008421,  3.16355067250,     3347.72597370060}, 
    {     0.00000006670,  5.07423317095,     8031.09226305840}, 
    {     0.00000008656,  4.33239148117,     3339.63210563160}, 
    {     0.00000007354,  6.17934256606,     3583.34103067380}, 
    {     0.00000005749,  3.67719823582,     8429.24126646660}, 
    {     0.00000006235,  3.54003325209,      692.15760122680}, 
    {     0.00000005458,  1.05139431657,     4933.20844033260}, 
    {     0.00000006132,  1.66182646558,     6525.80445396540}, 
    {     0.00000005197,  1.14841109166,       28.44918746780}, 
    {     0.00000004950,  5.28919125231,     6681.29216370240}, 
    {     0.00000005516,  6.12492946392,     2487.41604494780}, 
    {     0.00000004890,  3.10255139433,        5.52292430740}, 
    {     0.00000005354,  0.37154896863,    12832.75874170460}, 
    {     0.00000004751,  0.23374681550,       36.02786667740}, 
    {     0.00000006362,  2.11339432269,     5884.92684658320}, 
    {     0.00000004996,  2.44835744792,     5099.26550511660}, 
    {     0.00000004952,  5.69770765577,     6681.15754309680}, 
    {     0.00000004678,  0.27799012787,    10018.31416175040}, 
    {     0.00000004746,  0.00950199989,     7210.91581849420}, 
    {     0.00000004862,  5.60331599025,     6467.92575796160}, 
    {     0.00000005544,  2.00929051393,      522.57741809380}, 
    {     0.00000004998,  1.51094959078,     1744.42598441520}, 
    {     0.00000005397,  0.18842154970,     2942.46342329160}, 
    {     0.00000004098,  3.95776844736,        3.88133535800}, 
    {     0.00000005414,  5.66147396313,    23384.28698689860}, 
    {     0.00000005467,  0.19258681316,     7632.94325965020}, 
    {     0.00000004305,  2.89452294830,     2810.92146160520}, 
    {     0.00000004118,  1.59475420886,     7234.79425624200}, 
    {     0.00000004489,  4.16951490492,     2906.90068882300}, 
    {     0.00000005277,  2.22681020305,     3127.31333126180}, 
    {     0.00000003882,  2.26433789475,     2699.73481931760}, 
    {     0.00000003544,  1.76658498504,     1758.65307841680}, 
    {     0.00000003408,  2.65743533541,     4929.68532198360}, 
    {     0.00000004336,  4.43081904792,      640.87760738220}, 
    {     0.00000003804,  2.91373968131,    15643.68020330980}, 
    {     0.00000003176,  1.75893480952,     9595.23908922340}, 
    {     0.00000003309,  6.13831291678,    10419.98628350760}, 
    {     0.00000003077,  2.56194751001,     7064.12138562280}, 
    {     0.00000003236,  2.32387839882,     5085.03841111500}, 
    {     0.00000003284,  2.86216479710,     7740.60678358880}, 
    {     0.00000002958,  1.27767445188,      574.34479833480}, 
    {     0.00000002805,  0.43144651568,     5828.02847164760}, 
    {     0.00000002851,  0.98625869565,     3191.04922956520}, 
    {     0.00000003324,  2.59010987850,     2118.76386037840}, 
    {     0.00000003039,  1.86739127757,        7.04623669800}, 
    {     0.00000002738,  1.76460911547,      639.89728631400}, 
    {     0.00000002757,  3.70511041849,    10021.85453375160}, 
    {     0.00000003376,  1.53123149565,     6674.11130639880}, 
    {     0.00000002757,  1.67433972403,    10021.82002644720}, 
    {     0.00000002670,  3.11556212899,     6836.64525283380}, 
    {     0.00000002583,  3.77302627584,     2921.12778282460}, 
    {     0.00000002510,  0.30461555756,     3475.67750673520}, 
    {     0.00000002288,  2.81266012379,     7875.67186362420}, 
    {     0.00000002411,  0.97123911611,     3319.83703120740}, 
    {     0.00000002410,  2.95969382172,     6682.20517446780}, 
    {     0.00000002211,  0.61268074323,    10973.55568635000}, 
    {     0.00000002246,  4.12573972297,       59.37386191360}, 
    {     0.00000002183,  2.17530786579,    15113.98923821520}, 
    {     0.00000002445,  5.91435376684,     5331.35744374080}, 
    {     0.00000001944,  5.47623245699,    11371.70468975820}, 
    {     0.00000002390,  3.87952069289,     3355.86489788480}, 
    {     0.00000001904,  5.11178589044,     1066.49547719000}, 
    {     0.00000002302,  1.15940039520,     3320.25710730100}, 
    {     0.00000001955,  5.88703346758,     6894.52394883760}, 
    {     0.00000001837,  3.07635198966,     3325.35995551480}, 
    {     0.00000002131,  2.99610007510,     6254.62666252360}, 
    {     0.00000001807,  4.98332871905,     1648.44675719740}, 
    {     0.00000002133,  1.91321292871,     8969.56889691100}, 
    {     0.00000001936,  3.55090266368,     3767.21061757580}, 
    {     0.00000001989,  5.37314833955,      206.18554843720}, 
    {     0.00000001674,  5.49537183178,      266.60704172180}, 
    {     0.00000001732,  1.81246269542,      536.80451209540}, 
    {     0.00000001645,  1.32190162152,     3264.34635542420}, 
    {     0.00000001715,  3.25682611470,     7903.07341972100}, 
    {     0.00000001560,  5.75414697537,     3360.96774609859}, 
    {     0.00000001581,  1.72981711161,     3134.42687826260}, 
    {     0.00000001498,  4.89621878281,     9830.38901398780}, 
    {     0.00000001549,  5.85472144829,       20.77539549240}, 
    {     0.00000001685,  2.43562432843,     3120.19978426100}, 
    {     0.00000001548,  1.54152974975,     8425.65083781480}, 
    {     0.00000002012,  5.94532644656,    13365.97282514820}, 
    {     0.00000001972,  3.11534406510,     3361.38782219220}, 
    {     0.00000001391,  2.24268252285,     3344.20285535160}, 
    {     0.00000001369,  3.07997599503,     6127.65545055720}, 
    {     0.00000001365,  4.57979419810,    10818.13528691580}, 
    {     0.00000001361,  1.18605362322,    14584.29827312060}, 
    {     0.00000001376,  5.49004047305,      170.67287061920}, 
    {     0.00000001739,  2.01930737454,    10575.40668294180}, 
    {     0.00000001699,  5.63673097080,     6158.64743530580}, 
    {     0.00000001291,  5.91024520902,     9808.53818466140}, 
    {     0.00000001399,  1.81907706393,     3337.02199804800}, 
    {     0.00000001413,  4.50285394080,     5729.50644714900}, 
    {     0.00000001481,  6.04716796278,    12964.30070339100}, 
    {     0.00000001218,  0.82624604661,      419.48464387520}, 
    {     0.00000001406,  1.05089075450,     6438.49624942560}, 
    {     0.00000001190,  3.52559223977,     6688.33840040040}, 
    {     0.00000001263,  1.48624507606,     8439.87793181640}, 
    {     0.00000001145,  4.89771219093,      220.41264243880}, 
    {     0.00000001131,  6.19294401266,     6144.42034130420}, 
    {     0.00000001156,  2.23033209084,     8955.34180290940}, 
    {     0.00000001128,  3.44445874016,    10177.25767953360}, 
    {     0.00000001144,  5.29922202930,       27.40155609680}, 
    {     0.00000001098,  2.82106200873,     4569.57454002200}, 
    {     0.00000001271,  4.58458799479,     6247.51311552280}, 
    {     0.00000001352,  2.14065534125,    11243.68584642080}, 
    {     0.00000001297,  0.44389550166,       87.30820453981}, 
    {     0.00000001118,  1.96366629239,     6298.32832117640}, 
    {     0.00000001065,  2.89853673240,    10404.73381232260}, 
    {     0.00000001027,  4.79279924388,     3914.95722503460}, 
    {     0.00000001034,  3.73200738994,    10213.28554621100}, 
    {     0.00000001152,  4.14340380812,     6261.74020952440}, 
    {     0.00000000993,  0.22568223151,     3230.40610548040}, 
    {     0.00000001305,  3.67646278246,     2301.58581590939}, 
    {     0.00000001138,  5.11767079744,     4562.46099302120}, 
    {     0.00000000922,  0.46241803393,    13358.92658845020}, 
    {     0.00000001275,  5.14327521504,     2693.60159338500}, 
    {     0.00000000912,  1.23133665160,      103.09277421860}, 
    {     0.00000000953,  1.52860938585,     3369.06161416760}, 
    {     0.00000001009,  3.29653387473,     3178.14579056760}, 
    {     0.00000000893,  1.35062914664,     1214.73501932060}, 
    {     0.00000000918,  2.45577302887,    13916.01910964160}, 
    {     0.00000000969,  1.69080418858,       43.71891230500}, 
    {     0.00000000896,  5.62906563965,    10021.90459040220}, 
    {     0.00000000853,  5.94370893753,    12168.00269657460}, 
    {     0.00000000931,  0.24120697444,     6923.95345737360}, 
    {     0.00000000912,  1.10368236991,       29.42950853600}, 
    {     0.00000000816,  4.65205672982,     2707.82868738660}, 
    {     0.00000000801,  4.81849322003,      533.21408344360}, 
    {     0.00000000764,  6.08667124637,     2384.32327072920}, 
    {     0.00000000753,  1.03238937619,    14314.16811304980}, 
    {     0.00000000757,  2.06149804917,    12935.85151592320}, 
    {     0.00000000924,  0.69558587744,    16173.37116840440}, 
    {     0.00000000786,  3.91108639997,     9225.53927328300}, 
    {     0.00000000697,  4.07135509749,     5202.35827933520}, 
    {     0.00000000894,  6.03747462616,    10021.76996979660}, 
    {     0.00000000814,  2.01020002407,     9866.41688066520}, 
    {     0.00000000871,  4.45409720021,     3316.73398895200}, 
    {     0.00000000694,  6.01416161518,    26724.89941359840}, 
    {     0.00000000744,  1.39400789085,     8273.82086703240}, 
    {     0.00000000666,  3.02544526662,     1039.02661079040}, 
    {     0.00000000727,  3.27505135694,    18984.29263000960}, 
    {     0.00000000654,  2.83655009806,      107.66352393860}, 
    {     0.00000000680,  1.98065653254,     1228.96211332220}, 
    {     0.00000000829,  0.36839516637,    10551.52824519400}, 
    {     0.00000000585,  0.10314990118,      111.18664228760}, 
    {     0.00000000566,  1.59185176054,     2391.43681773000}, 
    {     0.00000000555,  2.70920251256,     4555.34744602040}, 
    {     0.00000000696,  2.89495274268,     2648.45482547300}, 
    {     0.00000000532,  5.65094737994,     6034.21402008480}, 
    {     0.00000000557,  5.08729863960,     1903.43681250120}, 
    {     0.00000000570,  4.59896697040,     6680.24453233140}, 
    {     0.00000000519,  0.20293365239,    13760.59871020740}, 
    {     0.00000000697,  3.87262209056,    13517.87010623340}, 
    {     0.00000000506,  3.20689286673,    11081.21921028860}, 
    {     0.00000000518,  2.85627321259,     5459.37628707820}, 
    {     0.00000000642,  5.19540766185,     6048.44111408640}, 
    {     0.00000000490,  2.42075152031,     3364.49086444760}, 
    {     0.00000000671,  3.69379654960,     3335.08950239240}, 
    {     0.00000000526,  0.23465052151,       51.28033786241}, 
    {     0.00000000483,  1.56485227643,     1964.83862685400}, 
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    {     0.00000000031,  0.88233421548,     3340.18254357310}, 
    {     0.00000000025,  0.83746118261,    12725.45343477500}, 
    {     0.00000000027,  5.67024059955,     1478.86657406440}, 
    {     0.00000000027,  0.42473501075,    33406.12426699800}, 
    {     0.00000000026,  2.15914082099,     3987.62326001460}, 
    {     0.00000000025,  2.91073064727,     3212.59358336240}, 
    {     0.00000000027,  4.12996350734,    13383.22510229160}, 
    {     0.00000000027,  6.05316799952,    13286.18363552360}, 
    {     0.00000000027,  5.81931319013,    24341.52831745660}, 
    {     0.00000000029,  4.41519700273,    16894.51039961060}, 
    {     0.00000000024,  0.20360604382,     3229.42578441220}, 
    {     0.00000000024,  2.10152754634,    14955.04572043200}, 
    {     0.00000000031,  5.90226054729,    11128.97608578420}, 
    {     0.00000000023,  3.37817298437,     6850.80503653260}, 
    {     0.00000000031,  0.35678160238,    31570.79964939120}, 
    {     0.00000000023,  2.38961518808,    23024.17620493700}, 
    {     0.00000000029,  3.03470840975,    22747.29071487440}, 
    {     0.00000000026,  0.51379054479,    29978.20363575840}, 
    {     0.00000000023,  4.26635202793,     3296.89351439480}, 
    {     0.00000000027,  2.64320191197,    24093.27678917520}, 
    {     0.00000000023,  4.96777735461,      799.82112516540}, 
    {     0.00000000024,  3.32945091041,    12140.60114047780}, 
    {     0.00000000025,  3.30212831704,     6740.59871531320}, 
    {     0.00000000023,  5.51381740402,    33561.54466643220}, 
    {     0.00000000023,  0.28172423109,     6593.91664885980}, 
    {     0.00000000022,  5.48861732897,    30376.35263916660}, 
    {     0.00000000023,  2.40580065766,     3344.11829139661}, 
    {     0.00000000028,  5.87506884260,     7747.72033058960}, 
    {     0.00000000021,  2.40354177453,     3304.00706139560}, 
    {     0.00000000024,  1.63482389429,     7483.58877584580}, 
    {     0.00000000028,  1.56312692708,    43340.65334255760}, 
    {     0.00000000022,  5.32476938106,    12928.73796892240}, 
    {     0.00000000026,  3.86983068409,    11353.89216764020}, 
    {     0.00000000023,  4.43657224846,     3344.15279870100}, 
    {     0.00000000021,  3.66824260126,    14951.52260208300}, 
    {     0.00000000022,  0.10813974117,    15423.26756087100}, 
    {     0.00000000025,  5.63091190933,     3416.87849797540}, 
    {     0.00000000025,  1.57746144847,    11567.19126307820}, 
    {     0.00000000026,  2.50180659493,    21791.69097326579}, 
    {     0.00000000022,  4.94823700773,     6681.64492949320}, 
    {     0.00000000026,  0.84448534014,     3397.51080163540}, 
    {     0.00000000021,  4.33866377991,    12729.66596748600}, 
    {     0.00000000021,  0.37058306281,     3391.89276456221}, 
    {     0.00000000022,  1.64362371744,     8852.24902869080}, 
    {     0.00000000027,  0.10733929729,     5195.24473233440}, 
    {     0.00000000021,  1.13140972844,    19403.77727388480}, 
    {     0.00000000026,  2.01526337234,     5032.77809620220}, 
    {     0.00000000021,  5.55525732543,    41748.05732892480}, 
    {     0.00000000021,  2.07959936360,    15106.87569121440}, 
    {     0.00000000024,  3.60866487742,    10006.58480891440}, 
    {     0.00000000028,  5.64135432549,    12516.36687204800}, 
    {     0.00000000027,  5.93032400892,     3074.00538497800}, 
    {     0.00000000025,  3.74768371499,     3232.94890276120}, 
    {     0.00000000022,  3.15578357220,    13366.04013545100}, 
    {     0.00000000021,  3.34013182507,    20752.66436247540}, 
    {     0.00000000026,  1.21869004343,     3377.21779200400}, 
    {     0.00000000024,  2.12604737559,     3171.03224356680}, 
    {     0.00000000022,  4.02124729955,    30774.50164257480}, 
    {     0.00000000024,  3.74309736843,     6747.71226231400}, 
    {     0.00000000023,  2.20705996255,    23553.86717003160}, 
    {     0.00000000021,  3.57070941130,    37895.42629036740}, 
    {     0.00000000023,  2.56549590800,    21192.36415686840}, 
    {     0.00000000021,  3.34401260695,    15010.89646399660}, 
    {     0.00000000019,  2.58752283276,    36261.27948574980}, 
    {     0.00000000021,  5.93180632509,    42146.20633233299}, 
    {     0.00000000018,  1.24405924793,     6768.53305793940}, 
    {     0.00000000019,  2.79026853354,    39203.74290904139}, 
    {     0.00000000024,  2.19710154155,    34513.26307268280}, 
    {     0.00000000020,  1.69850924464,    49225.58018914080}, 
    {     0.00000000018,  1.32432984119,    13497.51478683460}, 
    {     0.00000000018,  2.46520012266,     6944.30877677240}, 
    {     0.00000000018,  5.07942001013,     3337.07205469860}, 
    {     0.00000000018,  5.00983720257,     1655.56030419820}, 
    {     0.00000000018,  0.78739197008,    19676.45023123640}, 
    {     0.00000000018,  0.05420901908,     2142.64229812620}, 
};


static const struct ln_vsop mars_longitude_l2[LONG_L2] = {
    {     0.00058152577,  2.04961712429,     3340.61242669980}, 
    {     0.00013459579,  2.45738706163,     6681.22485339960}, 
    {     0.00002432575,  2.79737979284,    10021.83728009940}, 
    {     0.00000401065,  3.13581149963,    13362.44970679920}, 
    {     0.00000451384,  0.00000000000,        0.00000000000}, 
    {     0.00000222025,  3.19437046607,        3.52311834900}, 
    {     0.00000120954,  0.54327128607,      155.42039943420}, 
    {     0.00000062971,  3.47765178989,    16703.06213349900}, 
    {     0.00000053644,  3.54171478781,     3344.13554504880}, 
    {     0.00000034273,  6.00208464365,     2281.23049651060}, 
    {     0.00000031659,  4.14001980084,      191.44826611160}, 
    {     0.00000029839,  1.99838739380,      796.29800681640}, 
    {     0.00000023172,  4.33401932281,      242.72860397400}, 
    {     0.00000021663,  3.44500841809,      398.14900340820}, 
    {     0.00000016050,  6.11000263211,     2146.16541647520}, 
    {     0.00000020369,  5.42202383442,      553.56940284240}, 
    {     0.00000014924,  6.09549588012,     3185.19202726560}, 
    {     0.00000016229,  0.65685105422,        0.98032106820}, 
    {     0.00000014317,  2.61898820749,     1349.86740965880}, 
    {     0.00000014411,  4.01941740099,      951.71840625060}, 
    {     0.00000011944,  3.86196758615,     6684.74797174860}, 
    {     0.00000015655,  1.22093822826,     1748.01641306700}, 
    {     0.00000011261,  4.71857181601,     2544.31441988340}, 
    {     0.00000013360,  0.60151621438,     1194.44701022460}, 
    {     0.00000010395,  0.25075540193,      382.89653222320}, 
    {     0.00000009415,  0.68050215057,     1059.38193018920}, 
    {     0.00000009580,  3.82256319681,    20043.67456019880}, 
    {     0.00000008996,  3.88272784458,     3738.76143010800}, 
    {     0.00000007498,  5.46428174266,     1751.53953141600}, 
    {     0.00000006499,  5.47802397833,     1592.59601363280}, 
    {     0.00000006307,  2.34134269478,     3097.88382272579}, 
    {     0.00000006864,  2.57523762859,     3149.16416058820}, 
    {     0.00000005871,  1.14862855780,        7.11354700080}, 
    {     0.00000006675,  2.37862627319,     4136.91043351620}, 
    {     0.00000004655,  4.43102251490,     6151.53388830500}, 
    {     0.00000004201,  3.68638044545,     5614.72937620960}, 
    {     0.00000004796,  2.89378142432,     3333.49887969900}, 
    {     0.00000004074,  6.12610105396,     5628.95647021120}, 
    {     0.00000003660,  4.06581319964,     1990.74501704100}, 
    {     0.00000003284,  2.79214099721,     3894.18182954220}, 
    {     0.00000003615,  2.46526861067,      529.69096509460}, 
    {     0.00000003214,  0.68469193035,     8962.45534991020}, 
    {     0.00000003087,  4.56932030502,     3496.03282613400}, 
    {     0.00000002918,  5.41494777349,     2914.01423582380}, 
    {     0.00000002925,  1.23098223044,     2787.04302385740}, 
    {     0.00000002808,  1.38431632694,     4292.33083295040}, 
    {     0.00000002652,  1.05282528913,     3341.59274776800}, 
    {     0.00000002920,  3.41297158184,     3337.08930835080}, 
    {     0.00000002423,  0.96484330240,     4535.05943692440}, 
    {     0.00000002311,  4.84742235872,     9492.14631500480}, 
    {     0.00000002597,  5.74792546254,     3340.59517304760}, 
    {     0.00000002190,  3.26596280325,      213.29909543800}, 
    {     0.00000002598,  1.49506860128,     3340.62968035200}, 
    {     0.00000002365,  4.18303842420,    10025.36039844840}, 
    {     0.00000002630,  4.67732434694,     3583.34103067380}, 
    {     0.00000002606,  2.64976204169,     2388.89402044920}, 
    {     0.00000001822,  0.97105743952,     1589.07289528380}, 
    {     0.00000002397,  1.04493547179,     4399.99435688900}, 
    {     0.00000002203,  0.16281603659,     6525.80445396540}, 
    {     0.00000002373,  4.26885534124,     7079.37385680780}, 
    {     0.00000002366,  0.00564620006,     4690.47983635860}, 
    {     0.00000001623,  4.95374152644,     5088.62883976680}, 
    {     0.00000002143,  0.47993241836,     2700.71514038580}, 
    {     0.00000001646,  4.94105214632,     1221.84856632140}, 
    {     0.00000001588,  1.11405721408,    12303.06777661000}, 
    {     0.00000001518,  0.11076145171,     2957.71589447660}, 
    {     0.00000001774,  3.80344931471,     3723.50895892300}, 
    {     0.00000001364,  3.86744855408,     6283.07584999140}, 
    {     0.00000001764,  2.51992889432,     2810.92146160520}, 
    {     0.00000001394,  2.73608766730,     7477.52286021600}, 
    {     0.00000001280,  5.47285286548,     6677.70173505060}, 
    {     0.00000001447,  2.97506973239,     6489.77658728800}, 
    {     0.00000001248,  3.77100223369,     2699.73481931760}, 
    {     0.00000001527,  2.92629955117,      640.87760738220}, 
    {     0.00000001197,  1.89205359446,     6681.24210705180}, 
    {     0.00000001418,  1.54599865534,     3347.72597370060}, 
    {     0.00000001423,  4.17063094406,    23384.28698689860}, 
    {     0.00000001042,  5.83283345776,     4933.20844033260}, 
    {     0.00000001196,  6.14479114175,     6681.20759974740}, 
    {     0.00000001153,  1.50265359557,      426.59819087600}, 
    {     0.00000001099,  3.80358943061,     3870.30339179440}, 
    {     0.00000000909,  3.81838122072,     5092.15195811580}, 
    {     0.00000001071,  5.04949161471,     5621.84292321040}, 
    {     0.00000000846,  3.82219998207,     3340.54511639700}, 
    {     0.00000001075,  3.81844135104,     3553.91152213780}, 
    {     0.00000000856,  3.42045045625,     3340.67973700260}, 
    {     0.00000000916,  1.91472787569,     3532.06069281140}, 
    {     0.00000000714,  4.26169501052,     9623.68827669120}, 
    {     0.00000000907,  4.12943952579,      162.46663613220}, 
    {     0.00000000653,  3.10816357251,     7234.79425624200}, 
    {     0.00000000792,  5.20659969594,       87.30820453981}, 
    {     0.00000000654,  1.57331630734,     2487.41604494780}, 
    {     0.00000000649,  2.78892909992,      574.34479833480}, 
    {     0.00000000648,  5.18111077100,    12832.75874170460}, 
    {     0.00000000707,  5.83195869320,     3339.63210563160}, 
    {     0.00000000520,  4.64660657418,     6836.64525283380}, 
    {     0.00000000660,  0.24998045706,     8969.56889691100}, 
    {     0.00000000640,  1.70935421799,     7632.94325965020}, 
    {     0.00000000528,  0.31105409350,     8031.09226305840}, 
    {     0.00000000510,  4.63676288319,    10419.98628350760}, 
    {     0.00000000604,  3.85002715377,     5486.77784317500}, 
    {     0.00000000514,  1.38796992796,     7740.60678358880}, 
    {     0.00000000462,  1.33678943112,     7875.67186362420}, 
    {     0.00000000495,  4.50170882091,      692.15760122680}, 
    {     0.00000000471,  1.42441365252,     6682.20517446780}, 
    {     0.00000000550,  4.41887772777,     5331.35744374080}, 
    {     0.00000000439,  1.25554168321,     4929.68532198360}, 
    {     0.00000000419,  5.44439060471,    10018.31416175040}, 
    {     0.00000000537,  1.46176527778,    15643.68020330980}, 
    {     0.00000000405,  1.57332289249,     6127.65545055720}, 
    {     0.00000000390,  3.81525595562,     6681.29216370240}, 
    {     0.00000000397,  4.62209715420,     7210.91581849420}, 
    {     0.00000000367,  1.00110839190,     6041.32756708560}, 
    {     0.00000000358,  0.15138024092,      639.89728631400}, 
    {     0.00000000369,  0.55699031997,    11773.37681151540}, 
    {     0.00000000433,  4.50587650409,    13365.97282514820}, 
    {     0.00000000472,  5.18372269228,     2301.58581590939}, 
    {     0.00000000389,  4.22520163179,     6681.15754309680}, 
    {     0.00000000366,  5.02827753161,     6923.95345737360}, 
    {     0.00000000326,  3.99284456376,     8955.34180290940}, 
    {     0.00000000320,  2.23597582782,    10021.85453375160}, 
    {     0.00000000321,  0.20524537430,    10021.82002644720}, 
    {     0.00000000337,  2.98232216826,     5729.50644714900}, 
    {     0.00000000323,  1.34413812795,     2118.76386037840}, 
    {     0.00000000338,  2.49683073767,     6438.49624942560}, 
    {     0.00000000322,  0.51214404564,     9866.41688066520}, 
    {     0.00000000274,  3.35270419822,     9830.38901398780}, 
    {     0.00000000271,  1.53180722885,     1039.02661079040}, 
    {     0.00000000271,  2.23239080465,     5828.02847164760}, 
    {     0.00000000255,  4.05578912871,     7064.12138562280}, 
    {     0.00000000245,  5.10524905635,     8429.24126646660}, 
    {     0.00000000262,  2.03073386216,     3767.21061757580}, 
    {     0.00000000254,  0.46317479341,     6298.32832117640}, 
    {     0.00000000249,  4.27544865193,     6894.52394883760}, 
    {     0.00000000232,  3.06292621291,    10818.13528691580}, 
    {     0.00000000241,  1.94265839706,     6688.33840040040}, 
    {     0.00000000204,  0.02615801903,     3914.95722503460}, 
    {     0.00000000206,  4.52434051121,    26724.89941359840}, 
    {     0.00000000244,  1.23370429435,     8432.76438481560}, 
    {     0.00000000246,  3.83080164245,     4562.46099302120}, 
    {     0.00000000236,  1.69741583748,     2942.46342329160}, 
    {     0.00000000183,  4.94847733715,    10177.25767953360}, 
    {     0.00000000200,  3.23521719204,     6674.11130639880}, 
    {     0.00000000206,  3.53318037860,    10575.40668294180}, 
    {     0.00000000203,  3.80703081380,     6467.92575796160}, 
    {     0.00000000173,  3.26078770157,     3981.49003408200}, 
    {     0.00000000160,  5.95148314584,      310.84079886840}, 
    {     0.00000000167,  2.15287688461,    10973.55568635000}, 
    {     0.00000000191,  0.77503447629,    15113.98923821520}, 
    {     0.00000000152,  4.35155334509,     3360.96774609859}, 
    {     0.00000000167,  2.41354473163,     3355.86489788480}, 
    {     0.00000000179,  4.59684946724,    12964.30070339100}, 
    {     0.00000000165,  1.93485741767,     3127.31333126180}, 
    {     0.00000000143,  0.30520037218,     1903.43681250120}, 
    {     0.00000000135,  1.64201243891,     3325.35995551480}, 
    {     0.00000000168,  5.98672368946,     3320.25710730100}, 
    {     0.00000000126,  0.06628028702,     9595.23908922340}, 
    {     0.00000000126,  5.09324195826,     3475.67750673520}, 
    {     0.00000000142,  2.22584385110,     3178.14579056760}, 
    {     0.00000000137,  5.52640508040,    16173.37116840440}, 
    {     0.00000000116,  5.54615744680,    13358.92658845020}, 
    {     0.00000000130,  6.12910259056,     8273.82086703240}, 
    {     0.00000000106,  5.74124915667,     2288.34404351140}, 
    {     0.00000000110,  4.00849488333,    13916.01910964160}, 
    {     0.00000000111,  4.15314444907,    10021.90459040220}, 
    {     0.00000000124,  1.03360247396,    18454.60166491500}, 
    {     0.00000000111,  1.81233800595,    18984.29263000960}, 
    {     0.00000000108,  4.01725736300,     5884.92684658320}, 
    {     0.00000000099,  0.69247362673,    12310.18132361080}, 
    {     0.00000000098,  2.52732520244,     3191.04922956520}, 
    {     0.00000000095,  6.00085009229,    14584.29827312060}, 
    {     0.00000000092,  4.38893173686,     9808.53818466140}, 
    {     0.00000000091,  1.72031299533,    11081.21921028860}, 
    {     0.00000000114,  4.11263836293,     6158.64743530580}, 
    {     0.00000000091,  1.71520550367,     1505.28780909299}, 
    {     0.00000000093,  5.66680963190,     3319.83703120740}, 
    {     0.00000000089,  4.96845061541,    13760.59871020740}, 
    {     0.00000000089,  0.44335699327,    11371.70468975820}, 
    {     0.00000000086,  2.99034396202,     7903.07341972100}, 
    {     0.00000000089,  5.87200048108,    16858.48253293320}, 
    {     0.00000000102,  4.55812091356,    10021.76996979660}, 
    {     0.00000000092,  1.59954108842,    24093.27678917520}, 
    {     0.00000000080,  0.23144257625,     9779.10867612540}, 
    {     0.00000000079,  4.65340786273,     6144.42034130420}, 
    {     0.00000000076,  0.49995616312,    13119.72110282519}, 
    {     0.00000000084,  5.55308493446,     3427.92063123960}, 
    {     0.00000000076,  4.52961122356,      708.98980227659}, 
    {     0.00000000072,  1.22310316961,     2274.11694950980}, 
    {     0.00000000097,  5.46490186895,    13517.87010623340}, 
    {     0.00000000073,  5.30141060834,     4845.90023579280}, 
    {     0.00000000070,  0.09877565579,     1437.17561419860}, 
    {     0.00000000093,  5.11228667278,    10551.52824519400}, 
    {     0.00000000075,  0.67412470168,    16460.33352952499}, 
    {     0.00000000068,  2.23465524386,    10213.28554621100}, 
    {     0.00000000079,  5.26872987203,      853.19638175200}, 
    {     0.00000000069,  0.59532377543,    12935.85151592320}, 
    {     0.00000000080,  1.78140455646,    10022.81760116760}, 
    {     0.00000000065,  1.38904078670,     3253.30422216000}, 
    {     0.00000000075,  6.03732407558,     5085.03841111500}, 
    {     0.00000000078,  2.75071312389,    19402.79695281660}, 
    {     0.00000000061,  1.49021039778,     5459.37628707820}, 
    {     0.00000000062,  2.50552301889,     5642.19824260920}, 
    {     0.00000000079,  1.57382509764,     8270.29774868340}, 
    {     0.00000000066,  0.35982344278,     7255.56965173440}, 
    {     0.00000000060,  0.51628343105,    13362.43245314700}, 
    {     0.00000000079,  3.84136206523,     2766.26762836500}, 
    {     0.00000000061,  1.35834394421,    19800.94595622480}, 
    {     0.00000000057,  2.63537932021,    14314.16811304980}, 
    {     0.00000000062,  6.23224285432,     9381.93999378540}, 
    {     0.00000000056,  3.92602466001,     4032.77002792660}, 
    {     0.00000000058,  4.80541369849,    16706.58525184800}, 
    {     0.00000000056,  1.07495829941,     3364.49086444760}, 
    {     0.00000000074,  3.11826754597,     1107.13880568480}, 
    {     0.00000000056,  5.92196461153,    21265.52312652020}, 
    {     0.00000000055,  0.69133485773,     3344.20285535160}, 
    {     0.00000000058,  0.03055561004,     3369.06161416760}, 
    {     0.00000000068,  1.89382886303,     9225.53927328300}, 
    {     0.00000000061,  4.41416512793,    22345.26037610820}, 
    {     0.00000000054,  5.99826659037,    21947.11137270000}, 
    {     0.00000000056,  1.90889246971,    12721.57209941700}, 
    {     0.00000000058,  0.64076710539,     3980.50971301380}, 
    {     0.00000000073,  1.53390867765,     9380.95967271720}, 
    {     0.00000000071,  1.55065593763,     3361.38782219220}, 
    {     0.00000000052,  4.45775383250,    10404.73381232260}, 
    {     0.00000000055,  0.25842078226,     3337.02199804800}, 
    {     0.00000000050,  0.62274445643,     7373.38245462640}, 
    {     0.00000000065,  2.99158486208,     3316.73398895200}, 
    {     0.00000000050,  2.91155201771,     8982.81066930900}, 
    {     0.00000000051,  2.53925124485,    13362.46696045140}, 
    {     0.00000000053,  1.75963973665,     2648.45482547300}, 
    {     0.00000000047,  3.74205609558,    33716.96506586640}, 
    {     0.00000000047,  2.33985323120,    16062.18452611680}, 
    {     0.00000000051,  4.76183443226,     8671.96987044060}, 
    {     0.00000000047,  3.61238635706,    30376.35263916660}, 
    {     0.00000000045,  3.17314820387,     2818.03500860600}, 
    {     0.00000000056,  0.85677332683,    17468.85519794540}, 
    {     0.00000000054,  1.68830003586,    11216.28429032400}, 
    {     0.00000000054,  1.32704907908,     8439.87793181640}, 
    {     0.00000000059,  3.89706899146,     5244.04923920100}, 
    {     0.00000000043,  1.45207414702,    24889.57479599160}, 
    {     0.00000000043,  4.93434500530,    14469.58851248400}, 
    {     0.00000000047,  0.63724859746,    15110.46611986620}, 
    {     0.00000000048,  1.93153003679,     9468.26787725700}, 
    {     0.00000000041,  0.80934461579,    13207.02930736500}, 
    {     0.00000000043,  0.86742732243,    20752.66436247540}, 
    {     0.00000000041,  3.35182836767,     9588.12554222260}, 
    {     0.00000000043,  3.19403696329,    22743.40937951640}, 
    {     0.00000000040,  3.80517212464,    28628.33622609960}, 
    {     0.00000000045,  3.44446459800,    14158.74771361560}, 
    {     0.00000000041,  5.33088551342,      765.79306444640}, 
    {     0.00000000038,  2.34719947252,    10028.95082710020}, 
    {     0.00000000037,  4.87740795169,    30065.51184029820}, 
    {     0.00000000042,  3.77822295434,     3503.07906283200}, 
    {     0.00000000037,  0.24131392245,     9168.64089834740}, 
    {     0.00000000037,  2.42831434862,     7107.82304427560}, 
    {     0.00000000039,  3.67137247569,    13171.00144068760}, 
    {     0.00000000037,  5.41610716116,    10264.56588407340}, 
    {     0.00000000047,  0.89637520949,    16703.04487984680}, 
    {     0.00000000041,  0.68153555810,    11766.26326451460}, 
    {     0.00000000046,  1.51332559161,     6040.34724601740}, 
    {     0.00000000037,  1.95319370926,     6702.00024889200}, 
    {     0.00000000036,  0.79575390273,    20597.24396304120}, 
    {     0.00000000035,  3.79593106555,     1066.49547719000}, 
    {     0.00000000035,  3.48692827125,     9070.11887384880}, 
    {     0.00000000035,  4.69051318198,    10235.13637553740}, 
    {     0.00000000034,  1.42262836561,    21795.21409161479}, 
    {     0.00000000047,  2.92683549770,    16703.07938715119}, 
    {     0.00000000044,  2.00401073062,    28230.18722269139}, 
    {     0.00000000033,  5.86775675864,    19513.98359510420}, 
    {     0.00000000035,  4.22435449199,     8584.66166590080}, 
    {     0.00000000044,  6.08581860630,     6660.44945790720}, 
    {     0.00000000033,  2.61681384731,     6696.47732458460}, 
    {     0.00000000034,  3.70456078721,    15664.03552270859}, 
    {     0.00000000043,  5.44670688059,     6816.28993343500}, 
    {     0.00000000037,  2.03776406606,    14556.89671702380}, 
    {     0.00000000037,  5.71433282530,     5099.26550511660}, 
    {     0.00000000041,  0.17225787246,    25287.72379939980}, 
    {     0.00000000031,  2.30685466428,    10042.61267559180}, 
    {     0.00000000034,  0.72658199838,    11780.49035851620}, 
    {     0.00000000030,  1.28426808967,    11243.68584642080}, 
    {     0.00000000030,  3.37226860046,    27832.03821928320}, 
    {     0.00000000030,  4.49208108982,     9499.25986200560}, 
    {     0.00000000032,  4.74490222844,    17256.63153634140}, 
    {     0.00000000031,  5.02978229455,    25685.87280280800}, 
    {     0.00000000029,  1.05521949715,    13936.79450513400}, 
    {     0.00000000029,  2.13159143713,    22324.90505670940}, 
    {     0.00000000034,  0.77946190155,    10596.18207843420}, 
    {     0.00000000028,  5.13684548975,    12012.58229714040}, 
    {     0.00000000029,  4.19390076272,     6106.88005506480}, 
    {     0.00000000030,  5.79496586838,    10156.90236013480}, 
    {     0.00000000030,  1.95532800090,     6665.97238221460}, 
    {     0.00000000030,  4.37086181476,    12295.95422960920}, 
    {     0.00000000037,  3.33119104614,    12323.42309600880}, 
    {     0.00000000032,  0.03328289020,    17924.91069982040}, 
    {     0.00000000031,  6.22551067475,     6660.86953400080}, 
    {     0.00000000027,  6.22583184601,    20199.09495963300}, 
    {     0.00000000027,  4.47604397206,    15508.61512327440}, 
    {     0.00000000027,  4.18952669137,    19004.64794940840}, 
    {     0.00000000029,  0.33347322113,    11614.43329373220}, 
    {     0.00000000027,  2.55492575464,    13553.89797291080}, 
    {     0.00000000027,  5.17429820364,    20047.19767854780}, 
    {     0.00000000026,  4.75069348623,     9485.03276800400}, 
    {     0.00000000028,  5.05646024487,    16304.91313009080}, 
    {     0.00000000026,  0.33571424841,     1758.65307841680}, 
    {     0.00000000026,  1.88254124807,     4379.63903749020}, 
    {     0.00000000026,  0.66164680044,     6677.63442474780}, 
    {     0.00000000027,  0.16359834714,    10001.06188460700}, 
    {     0.00000000026,  1.27240071340,    21548.96236929180}, 
    {     0.00000000027,  2.42251642195,     6518.75821726740}, 
    {     0.00000000025,  0.38159855574,    10001.48196070061}, 
    {     0.00000000025,  5.68892581324,     4193.80880845180}, 
    {     0.00000000025,  3.41513259489,     6657.34641565180}, 
    {     0.00000000031,  0.85409497605,    16276.46394262300}, 
    {     0.00000000025,  4.41986609477,    12168.00269657460}, 
    {     0.00000000030,  4.77047285234,    12722.55242048520}, 
    {     0.00000000028,  3.06003442590,     6247.51311552280}, 
    {     0.00000000025,  3.09863827375,    10037.08975128440}, 
    {     0.00000000025,  1.02575938018,    15650.79375031060}, 
    {     0.00000000024,  3.95596007260,     4936.79886898440}, 
    {     0.00000000024,  0.15547683375,    23141.55838292460}, 
    {     0.00000000024,  2.02621002883,     5989.06725217280}, 
    {     0.00000000030,  5.78174720450,    16699.53901514999}, 
    {     0.00000000026,  1.86541912366,    11610.91017538320}, 
    {     0.00000000026,  1.09364283303,     6684.81528205140}, 
    {     0.00000000025,  3.89771277869,     1052.26838318840}, 
    {     0.00000000027,  2.56503603603,    18052.92954315780}, 
    {     0.00000000023,  1.51797615340,    24491.42579258340}, 
    {     0.00000000023,  3.00396120711,    12566.15169998280}, 
    {     0.00000000022,  4.95564076891,    13362.38239649640}, 
    {     0.00000000026,  5.35396491473,    17101.21113690720}, 
    {     0.00000000025,  0.78394576420,     3863.18984479360}, 
    {     0.00000000029,  0.72436044897,     9638.94074787620}, 
    {     0.00000000023,  4.78936229419,    11925.27409260060}, 
    {     0.00000000028,  0.45519439131,     6709.67404086740}, 
    {     0.00000000026,  4.87772426583,    13149.15061136120}, 
    {     0.00000000023,  5.40586773017,    13892.14067189380}, 
    {     0.00000000023,  2.35248036676,    30774.50164257480}, 
    {     0.00000000028,  1.10862278422,     8425.65083781480}, 
    {     0.00000000023,  3.61712960620,     1581.95934828300}, 
    {     0.00000000026,  0.31100585552,     3603.69635007260}, 
    {     0.00000000020,  2.43389989577,    19406.67828817460}, 
    {     0.00000000025,  5.91413646106,     6680.24453233140}, 
    {     0.00000000020,  5.43460902247,    17395.21973472580}, 
    {     0.00000000025,  1.00211327228,     7321.12213971360}, 
    {     0.00000000020,  5.58281555175,    18606.49894600020}, 
    {     0.00000000025,  3.57752663624,     3873.82651014340}, 
    {     0.00000000021,  2.14222861506,    14421.83163698840}, 
    {     0.00000000020,  5.47581404162,    20735.83216142559}, 
    {     0.00000000021,  5.53809813850,    15265.88651930040}, 
    {     0.00000000019,  5.69034956533,    17013.90293236740}, 
    {     0.00000000019,  5.76144586324,    17085.95866572220}, 
    {     0.00000000022,  2.98924680598,     9602.35263622420}, 
    {     0.00000000019,  5.73996220529,     3651.45322556820}, 
    {     0.00000000018,  0.52367856726,    14054.60730802600}, 
    {     0.00000000022,  5.16650472247,     3376.64029337720}, 
    {     0.00000000020,  2.67348019896,    10448.43547097540}, 
    {     0.00000000018,  3.70248341637,    37057.57749256620}, 
    {     0.00000000018,  2.14231646843,    13363.43002786740}, 
    {     0.00000000020,  6.25669293739,     1744.42598441520}, 
    {     0.00000000020,  1.60190678685,    23296.97878235879}, 
    {     0.00000000023,  4.54770256231,    13362.51701710200}, 
    {     0.00000000024,  0.54356017220,     6475.03930496240}, 
    {     0.00000000023,  2.73656801737,     6261.74020952440}, 
    {     0.00000000018,  5.45243764566,    40000.04091585779}, 
    {     0.00000000018,  1.77799263643,     8799.98871377800}, 
    {     0.00000000018,  1.18266196226,    31172.65064598300}, 
    {     0.00000000019,  3.66181465270,     1596.18644228460}, 
    {     0.00000000018,  3.46673198156,     3546.79797513700}, 
    {     0.00000000022,  2.15272313802,     3335.08950239240}, 
    {     0.00000000018,  0.13829920233,     3877.41693879520}, 
    {     0.00000000020,  4.57210028361,     6701.58017279840}, 
    {     0.00000000019,  5.09290088720,     3205.54734666440}, 
    {     0.00000000016,  3.67355426368,    20995.39296644940}, 
    {     0.00000000016,  6.13550943291,     3134.42687826260}, 
    {     0.00000000016,  6.22620467137,    22854.59602180400}, 
    {     0.00000000016,  1.44137713060,     6460.81221096080}, 
    {     0.00000000015,  1.18753446282,     7203.80227149340}, 
    {     0.00000000016,  3.90125903944,     7322.10246078180}, 
    {     0.00000000015,  4.93156258719,     3304.58456002240}, 
    {     0.00000000017,  0.49763390696,    18208.34994259200}, 
    {     0.00000000017,  3.32863823640,     3333.56619000180}, 
    {     0.00000000014,  5.31587329158,    19645.52555679060}, 
    {     0.00000000017,  3.01193328720,     3344.49376205780}, 
    {     0.00000000016,  4.54660273048,     4392.88080988820}, 
    {     0.00000000013,  5.26350209812,    16702.99482319620}, 
    {     0.00000000016,  6.12947849429,    26087.90314157420}, 
    {     0.00000000013,  5.84447235851,      536.80451209540}, 
    {     0.00000000017,  4.09065954177,    16511.61386738740}, 
    {     0.00000000015,  5.73438221173,    14867.73751589219}, 
    {     0.00000000013,  2.54721959021,     6675.70192909220}, 
    {     0.00000000014,  1.31577259278,    21150.81336588360}, 
    {     0.00000000013,  2.12815796147,     3346.13535100720}, 
    {     0.00000000013,  3.59360902373,    12410.73130054860}, 
    {     0.00000000016,  5.67307416663,    11527.12508919240}, 
    {     0.00000000016,  0.84938642384,    10184.30391623160}, 
    {     0.00000000013,  6.16919624193,     3077.52850332700}, 
    {     0.00000000014,  3.93053280186,     3312.16323923200}, 
    {     0.00000000014,  2.55072089788,      206.18554843720}, 
    {     0.00000000013,  4.69830610865,    16703.12944380180}, 
    {     0.00000000012,  0.92968593112,    10713.99488132620}, 
    {     0.00000000011,  6.09331837551,     8827.39026987480}, 
    {     0.00000000014,  3.77650372404,    17499.36014031540}, 
    {     0.00000000011,  1.09619387864,    16547.64173406480}, 
    {     0.00000000011,  5.05016560122,    24076.44458812540}, 
    {     0.00000000015,  6.16612008928,     3347.65866339780}, 
    {     0.00000000011,  1.92845507292,    11769.85369316640}, 
    {     0.00000000013,  1.01843193479,    10018.24685144760}, 
    {     0.00000000015,  0.92188099847,     3281.23856478620}, 
    {     0.00000000013,  5.19040439871,    16489.76303806100}, 
    {     0.00000000011,  0.29063320387,     2906.90068882300}, 
    {     0.00000000011,  5.65061614555,    13605.17831077320}, 
    {     0.00000000013,  5.06832582026,    13575.74880223720}, 
    {     0.00000000011,  5.42648525700,    17232.75309859360}, 
    {     0.00000000014,  2.18442424174,    12808.88030395680}, 
    {     0.00000000010,  3.12070301287,     2803.80791460440}, 
    {     0.00000000011,  1.35555533168,     2277.70737816160}, 
    {     0.00000000010,  5.89715293869,     6768.53305793940}, 
    {     0.00000000010,  5.93295499002,    23937.85638974100}, 
    {     0.00000000012,  1.20813089438,     3336.73109134180}, 
    {     0.00000000011,  2.56209057142,    13369.56325380000}, 
    {     0.00000000012,  0.50116227157,    34513.26307268280}, 
    {     0.00000000010,  4.37163145009,     3607.21946842160}, 
    {     0.00000000011,  4.03902225289,     4407.10790388980}, 
    {     0.00000000010,  4.18585556139,        0.01725365220}, 
    {     0.00000000011,  0.06058557016,    26880.31981303260}, 
    {     0.00000000011,  5.12397606143,    33406.12426699800}, 
    {     0.00000000011,  1.00077091959,    12979.55317457600}, 
    {     0.00000000010,  0.39595065439,    14955.04572043200}, 
    {     0.00000000011,  3.36133910370,    16894.51039961060}, 
    {     0.00000000010,  1.63992012008,      220.41264243880}, 
    {     0.00000000010,  5.76293648428,    31968.94865279940}, 
    {     0.00000000013,  1.44898528338,    10025.42770875120}, 
    {     0.00000000011,  4.36692917575,    34115.11406927460}, 
    {     0.00000000010,  4.84826192777,    12839.87228870540}, 
    {     0.00000000010,  1.85828895892,     6593.91664885980}, 
    {     0.00000000010,  5.75866529304,     6717.25272007700}, 
    {     0.00000000012,  4.33022696919,     7747.72033058960}, 
    {     0.00000000011,  5.96309733546,    20040.15144184979}, 
    {     0.00000000010,  3.58563293895,    20354.51535906720}, 
    {     0.00000000010,  4.88835260040,    10042.19259949820}, 
    {     0.00000000010,  2.48515633128,    25665.51748340920}, 
    {     0.00000000009,  1.77145376267,    32367.09765620760}, 
};


static const struct ln_vsop mars_longitude_l3[LONG_L3] = {
    {     0.00001467867,  0.44429839460,     3340.61242669980}, 
    {     0.00000692668,  0.88679887123,     6681.22485339960}, 
    {     0.00000189478,  1.28336839921,    10021.83728009940}, 
    {     0.00000041615,  1.64210455567,    13362.44970679920}, 
    {     0.00000022660,  2.05278956965,      155.42039943420}, 
    {     0.00000008126,  1.99049724299,    16703.06213349900}, 
    {     0.00000010455,  1.57992093693,        3.52311834900}, 
    {     0.00000004902,  2.82516875010,      242.72860397400}, 
    {     0.00000005379,  3.14159265359,        0.00000000000}, 
    {     0.00000003782,  2.01848153986,     3344.13554504880}, 
    {     0.00000003181,  4.59108786647,     3185.19202726560}, 
    {     0.00000003133,  0.65141319517,      553.56940284240}, 
    {     0.00000001698,  5.53803382831,      951.71840625060}, 
    {     0.00000001525,  5.71698515888,      191.44826611160}, 
    {     0.00000001451,  0.46068490220,      796.29800681640}, 
    {     0.00000001473,  2.33727441522,    20043.67456019880}, 
    {     0.00000001314,  5.36403056955,        0.98032106820}, 
    {     0.00000001178,  4.14644990348,     1349.86740965880}, 
    {     0.00000001138,  2.37914351932,     6684.74797174860}, 
    {     0.00000001046,  1.76915268602,      382.89653222320}, 
    {     0.00000000902,  5.35475854699,     1194.44701022460}, 
    {     0.00000000813,  2.74852234414,     1748.01641306700}, 
    {     0.00000000629,  6.08292992203,     3496.03282613400}, 
    {     0.00000000564,  1.87914711325,      398.14900340820}, 
    {     0.00000000566,  5.85439216540,        7.11354700080}, 
    {     0.00000000646,  3.17980126471,     3583.34103067380}, 
    {     0.00000000461,  5.99300094958,     2787.04302385740}, 
    {     0.00000000515,  1.00397565149,     3149.16416058820}, 
    {     0.00000000524,  4.94366714135,     6525.80445396540}, 
    {     0.00000000405,  1.25868884474,     2281.23049651060}, 
    {     0.00000000396,  2.33533869272,     3738.76143010800}, 
    {     0.00000000473,  0.85569341494,     4136.91043351620}, 
    {     0.00000000337,  5.42720231008,     1059.38193018920}, 
    {     0.00000000312,  3.71767667252,     3097.88382272579}, 
    {     0.00000000280,  5.77799085447,     3341.59274776800}, 
    {     0.00000000282,  2.71397487800,    10025.36039844840}, 
    {     0.00000000215,  5.72936855193,     4535.05943692440}, 
    {     0.00000000213,  2.52113312108,     1990.74501704100}, 
    {     0.00000000253,  2.68513749891,    23384.28698689860}, 
    {     0.00000000271,  1.11020953644,     2388.89402044920}, 
    {     0.00000000186,  4.87399580961,     2957.71589447660}, 
    {     0.00000000178,  3.91361250070,     1592.59601363280}, 
    {     0.00000000175,  0.87350226081,     3894.18182954220}, 
    {     0.00000000191,  4.57651964364,     3337.08930835080}, 
    {     0.00000000166,  2.74261580519,     7079.37385680780}, 
    {     0.00000000132,  1.21969793594,     7477.52286021600}, 
    {     0.00000000176,  5.82269855073,     4399.99435688900}, 
    {     0.00000000144,  1.41866825837,     6489.77658728800}, 
    {     0.00000000116,  3.26440506489,     9492.14631500480}, 
    {     0.00000000110,  5.25036780309,     8962.45534991020}, 
    {     0.00000000109,  2.69848602723,     6151.53388830500}, 
    {     0.00000000099,  3.53126616352,     6923.95345737360}, 
    {     0.00000000094,  5.83398846011,    12303.06777661000}, 
    {     0.00000000082,  5.71976568172,     4292.33083295040}, 
    {     0.00000000082,  0.07031928087,     6127.65545055720}, 
    {     0.00000000079,  5.82605787124,     1589.07289528380}, 
    {     0.00000000086,  5.29348370173,     9866.41688066520}, 
    {     0.00000000101,  0.00033367659,     3347.72597370060}, 
    {     0.00000000076,  4.33662644570,     4933.20844033260}, 
    {     0.00000000066,  4.98095301409,     5486.77784317500}, 
    {     0.00000000066,  1.74326529570,     3870.30339179440}, 
    {     0.00000000059,  1.47406427963,     7234.79425624200}, 
    {     0.00000000065,  4.13790023458,     3340.59517304760}, 
    {     0.00000000066,  6.17474740457,     6682.20517446780}, 
    {     0.00000000065,  6.16873733389,     3340.62968035200}, 
    {     0.00000000061,  3.04498621253,    13365.97282514820}, 
    {     0.00000000057,  0.34435287503,     6681.24210705180}, 
    {     0.00000000052,  3.10877560472,    10419.98628350760}, 
    {     0.00000000053,  1.49212635155,     5729.50644714900}, 
    {     0.00000000052,  6.16231097097,     7740.60678358880}, 
    {     0.00000000057,  4.59725498148,     6681.20759974740}, 
    {     0.00000000047,  6.08280843167,     7875.67186362420}, 
    {     0.00000000046,  2.22700618360,     6283.07584999140}, 
    {     0.00000000042,  4.17552906301,     4690.47983635860}, 
    {     0.00000000053,  4.86310998799,     5621.84292321040}, 
    {     0.00000000039,  3.01231289993,    26724.89941359840}, 
    {     0.00000000044,  1.83807443880,     3723.50895892300}, 
    {     0.00000000045,  3.66313190536,    12832.75874170460}, 
    {     0.00000000049,  2.90677449550,     5331.35744374080}, 
    {     0.00000000041,  5.09013551341,     8969.56889691100}, 
    {     0.00000000035,  1.80197655191,     9830.38901398780}, 
    {     0.00000000036,  6.20064893632,     6836.64525283380}, 
    {     0.00000000041,  4.73855176222,     6677.70173505060}, 
    {     0.00000000043,  0.12056288166,     7632.94325965020}, 
    {     0.00000000036,  3.95211035317,     5092.15195811580}, 
    {     0.00000000041,  1.02183708699,     3339.63210563160}, 
    {     0.00000000032,  6.08260895536,     4929.68532198360}, 
    {     0.00000000029,  1.62918363864,    10818.13528691580}, 
    {     0.00000000033,  5.28926114198,     6298.32832117640}, 
    {     0.00000000035,  2.19127331195,     3553.91152213780}, 
    {     0.00000000031,  1.71403126017,     6674.11130639880}, 
    {     0.00000000027,  2.59859773299,     9623.68827669120}, 
    {     0.00000000037,  6.26363818135,    15643.68020330980}, 
    {     0.00000000026,  0.41795219764,     6688.33840040040}, 
    {     0.00000000025,  2.61050876047,     8955.34180290940}, 
    {     0.00000000024,  2.72770670140,     7210.91581849420}, 
    {     0.00000000022,  0.56923205824,     3333.49887969900}, 
    {     0.00000000024,  1.08927112722,    13362.46696045140}, 
    {     0.00000000024,  1.27631664508,     2146.16541647520}, 
    {     0.00000000021,  2.25460322522,     6681.29216370240}, 
    {     0.00000000021,  1.21340354488,      529.69096509460}, 
    {     0.00000000019,  2.21770037001,     3340.54511639700}, 
    {     0.00000000019,  0.66923624814,    10021.85453375160}, 
    {     0.00000000019,  4.96725594495,    10021.82002644720}, 
    {     0.00000000021,  2.66383165337,     6681.15754309680}, 
    {     0.00000000019,  5.34528034089,    13362.43245314700}, 
    {     0.00000000020,  4.05200075148,    16173.37116840440}, 
    {     0.00000000018,  6.12827330419,     2118.76386037840}, 
    {     0.00000000019,  1.81106961128,     3340.67973700260}, 
    {     0.00000000023,  3.65530501555,     5884.92684658320}, 
    {     0.00000000017,  3.49526304116,    13760.59871020740}, 
    {     0.00000000017,  2.19106157796,    13171.00144068760}, 
    {     0.00000000018,  2.57298367742,     6894.52394883760}, 
    {     0.00000000015,  3.38406160245,    16706.58525184800}, 
    {     0.00000000020,  5.66097673948,    11773.37681151540}, 
    {     0.00000000016,  5.03015729119,     8031.09226305840}, 
    {     0.00000000018,  5.85813180984,    15113.98923821520}, 
    {     0.00000000015,  0.77504052248,    10028.95082710020}, 
    {     0.00000000015,  0.57957141835,    10973.55568635000}, 
    {     0.00000000014,  0.24974244701,     5088.62883976680}, 
    {     0.00000000018,  3.07924421940,    12964.30070339100}, 
    {     0.00000000015,  2.68623334057,    10021.90459040220}, 
    {     0.00000000015,  3.09469457587,    10021.76996979660}, 
    {     0.00000000013,  3.93023649028,    10264.56588407340}, 
    {     0.00000000013,  5.65831284328,    13207.02930736500}, 
    {     0.00000000013,  1.84300811278,     9070.11887384880}, 
    {     0.00000000014,  0.29740739896,    18984.29263000960}, 
    {     0.00000000013,  2.52001940946,     7064.12138562280}, 
    {     0.00000000013,  3.67191025834,     3320.25710730100}, 
    {     0.00000000013,  0.38182731490,    11081.21921028860}, 
    {     0.00000000015,  5.65316717493,     9638.94074787620}, 
    {     0.00000000015,  1.98431328230,    14158.74771361560}, 
    {     0.00000000012,  5.41217638500,    12310.18132361080}, 
    {     0.00000000013,  2.16005341496,     3503.07906283200}, 
    {     0.00000000013,  2.04039005845,     3360.96774609859}, 
    {     0.00000000012,  3.10587105006,    10551.52824519400}, 
    {     0.00000000012,  0.10001647761,     3355.86489788480}, 
    {     0.00000000011,  2.14032736093,    10014.72373309860}, 
    {     0.00000000011,  1.79726060971,     6438.49624942560}, 
    {     0.00000000014,  0.17608466993,    11216.28429032400}, 
    {     0.00000000011,  3.38101843423,    30065.51184029820}, 
    {     0.00000000010,  0.14034808917,     5459.37628707820}, 
    {     0.00000000012,  1.39972628733,     7322.10246078180}, 
    {     0.00000000010,  5.01174496801,     8432.76438481560}, 
    {     0.00000000010,  4.85370121323,     8827.39026987480}, 
    {     0.00000000012,  1.85790840539,    10575.40668294180}, 
    {     0.00000000011,  5.68929132609,     2544.31441988340}, 
    {     0.00000000013,  0.11973675130,     8270.29774868340}, 
    {     0.00000000010,  3.45366828680,     8671.96987044060}, 
    {     0.00000000010,  1.63456773166,     6467.92575796160}, 
    {     0.00000000012,  0.48472196247,     9468.26787725700}, 
    {     0.00000000010,  1.79285582925,     3981.49003408200}, 
    {     0.00000000012,  4.35157153740,    13358.92658845020}, 
    {     0.00000000012,  4.70754717702,     8273.82086703240}, 
    {     0.00000000009,  5.67195388102,     6041.32756708560}, 
    {     0.00000000011,  0.28291831064,    10022.81760116760}, 
    {     0.00000000012,  0.19598354169,     3767.21061757580}, 
    {     0.00000000009,  0.79888103600,     7107.82304427560}, 
    {     0.00000000009,  2.63887133820,     6040.34724601740}, 
    {     0.00000000010,  4.24040970796,    10018.31416175040}, 
    {     0.00000000008,  4.41344390506,     3532.06069281140}, 
    {     0.00000000009,  4.61082143531,     6254.62666252360}, 
    {     0.00000000010,  3.14867092101,    12295.95422960920}, 
    {     0.00000000008,  4.30808895338,    13517.87010623340}, 
    {     0.00000000007,  3.72930971887,    20047.19767854780}, 
    {     0.00000000007,  5.31461308603,     3980.50971301380}, 
    {     0.00000000007,  4.41228197932,    19513.98359510420}, 
    {     0.00000000006,  0.70081238478,    22324.90505670940}, 
    {     0.00000000007,  3.46042125643,    16304.91313009080}, 
    {     0.00000000006,  4.18130136613,     9225.53927328300}, 
    {     0.00000000007,  2.07260074047,     2274.11694950980}, 
    {     0.00000000008,  4.84690285943,     5614.72937620960}, 
    {     0.00000000007,  5.81948406996,    18454.60166491500}, 
    {     0.00000000006,  4.58700022729,    12935.85151592320}, 
    {     0.00000000006,  3.09847010281,    10235.13637553740}, 
    {     0.00000000007,  5.65100333611,     3325.35995551480}, 
    {     0.00000000006,  3.88836191013,     8429.24126646660}, 
    {     0.00000000006,  6.08444137601,      426.59819087600}, 
    {     0.00000000007,  4.39290235530,    16699.53901514999}, 
    {     0.00000000006,  4.96952219943,    11614.43329373220}, 
    {     0.00000000007,  3.86534915027,    17101.21113690720}, 
    {     0.00000000005,  3.27691563611,      213.29909543800}, 
    {     0.00000000006,  2.22078885531,    13916.01910964160}, 
    {     0.00000000005,  5.40200843260,    11371.70468975820}, 
    {     0.00000000006,  3.73369549160,    33406.12426699800}, 
    {     0.00000000005,  1.76068977855,     1066.49547719000}, 
    {     0.00000000005,  3.34460420545,     4562.46099302120}, 
    {     0.00000000005,  5.87001587166,    16547.64173406480}, 
    {     0.00000000005,  2.58164780968,    10404.73381232260}, 
    {     0.00000000005,  0.95143416553,     6872.67311951120}, 
    {     0.00000000005,  3.29623418943,    13362.38239649640}, 
    {     0.00000000005,  4.15921606694,        0.01725365220}, 
    {     0.00000000005,  1.88015249528,    15508.61512327440}, 
    {     0.00000000005,  4.69029931558,     2700.71514038580}, 
};


static const struct ln_vsop mars_longitude_l4[LONG_L4] = {
    {     0.00000027242,  5.63997742320,     6681.22485339960}, 
    {     0.00000025511,  5.13956279086,     3340.61242669980}, 
    {     0.00000011147,  6.03556608878,    10021.83728009940}, 
    {     0.00000003190,  3.56206901204,      155.42039943420}, 
    {     0.00000003251,  0.12915616460,    13362.44970679920}, 
    {     0.00000000790,  0.48979114861,    16703.06213349900}, 
    {     0.00000000783,  1.31770747646,      242.72860397400}, 
    {     0.00000000500,  3.08200921500,     3185.19202726560}, 
    {     0.00000000374,  2.15499052115,      553.56940284240}, 
    {     0.00000000338,  6.23352693699,        3.52311834900}, 
    {     0.00000000199,  0.45348344109,     3344.13554504880}, 
    {     0.00000000168,  3.76870889622,     3496.03282613400}, 
    {     0.00000000171,  0.84135133604,    20043.67456019880}, 
    {     0.00000000115,  1.67425271260,     3583.34103067380}, 
    {     0.00000000080,  0.85706484335,     6684.74797174860}, 
    {     0.00000000091,  3.43800003890,     6525.80445396540}, 
    {     0.00000000062,  4.48712111677,     2787.04302385740}, 
    {     0.00000000043,  5.18700577258,     3097.88382272579}, 
    {     0.00000000047,  0.00000000000,        0.00000000000}, 
    {     0.00000000037,  1.18296722277,    23384.28698689860}, 
    {     0.00000000024,  4.29204464862,     6836.64525283380}, 
    {     0.00000000026,  1.20348583477,    10025.36039844840}, 
    {     0.00000000024,  5.60827511165,     4136.91043351620}, 
    {     0.00000000022,  5.74642710221,     3149.16416058820}, 
    {     0.00000000018,  2.03318579635,     6923.95345737360}, 
    {     0.00000000015,  4.26014468247,     3341.59274776800}, 
    {     0.00000000018,  2.33884195894,     3894.18182954220}, 
    {     0.00000000015,  0.76745028682,     3738.76143010800}, 
    {     0.00000000013,  3.78255342218,     9866.41688066520}, 
    {     0.00000000013,  4.84669665560,     6127.65545055720}, 
    {     0.00000000015,  5.90904577370,     2388.89402044920}, 
    {     0.00000000012,  4.04057703674,     4535.05943692440}, 
    {     0.00000000011,  3.87847882201,     1059.38193018920}, 
    {     0.00000000011,  6.15709897926,     6489.77658728800}, 
    {     0.00000000010,  1.72288144187,     9492.14631500480}, 
    {     0.00000000010,  1.57846217224,    13365.97282514820}, 
    {     0.00000000008,  2.41269301261,     1592.59601363280}, 
    {     0.00000000008,  3.38799237939,     2957.71589447660}, 
    {     0.00000000008,  6.09858519460,     7477.52286021600}, 
    {     0.00000000010,  1.26692397596,     1990.74501704100}, 
    {     0.00000000010,  1.19094173671,     7079.37385680780}, 
    {     0.00000000011,  4.27677188971,     4399.99435688900}, 
    {     0.00000000008,  4.14850970681,    13207.02930736500}, 
    {     0.00000000008,  1.54297406750,    26724.89941359840}, 
    {     0.00000000007,  0.26868468775,     9830.38901398780}, 
    {     0.00000000007,  0.08101546764,    10818.13528691580}, 
    {     0.00000000007,  2.42508289520,    10264.56588407340}, 
    {     0.00000000007,  5.57348066316,     6438.49624942560}, 
    {     0.00000000007,  4.62218969676,    10177.25767953360}, 
    {     0.00000000008,  0.34286691468,     3723.50895892300}, 
    {     0.00000000006,  1.60196605908,    10419.98628350760}, 
    {     0.00000000006,  4.33371839115,     4292.33083295040}, 
    {     0.00000000007,  4.61281837777,     7875.67186362420}, 
    {     0.00000000006,  4.67857531326,     2544.31441988340}, 
    {     0.00000000007,  1.51290306715,     5331.35744374080}, 
    {     0.00000000006,  4.16295898909,    12303.06777661000}, 
    {     0.00000000006,  4.52108494056,     3532.06069281140}, 
    {     0.00000000006,  4.66651817095,     7740.60678358880}, 
    {     0.00000000005,  6.26581073985,     5729.50644714900}, 
    {     0.00000000005,  2.75621336253,     4690.47983635860}, 
    {     0.00000000005,  2.78107610422,     4933.20844033260}, 
    {     0.00000000005,  4.63812650627,     6682.20517446780}, 
    {     0.00000000005,  5.81870543856,     2146.16541647520}, 
    {     0.00000000004,  4.97648147254,     3347.72597370060}, 
    {     0.00000000004,  1.92818801589,    16706.58525184800}, 
    {     0.00000000004,  3.51723776816,     5486.77784317500}, 
    {     0.00000000004,  4.37622919020,     3337.08930835080}, 
    {     0.00000000003,  3.74520053012,     6298.32832117640}, 
    {     0.00000000003,  4.94059407345,    11081.21921028860}, 
    {     0.00000000003,  5.20767397767,     9468.26787725700}, 
    {     0.00000000002,  5.60261719076,     3333.49887969900}, 
    {     0.00000000003,  6.08152672681,     3339.63210563160}, 
    {     0.00000000002,  1.90275008409,    30065.51184029820}, 
    {     0.00000000003,  3.36064341832,     5621.84292321040}, 
    {     0.00000000002,  0.01141937510,    10551.52824519400}, 
};


static const struct ln_vsop mars_longitude_l5[LONG_L5] = {
    {     0.00000000762,  4.03556368806,     6681.22485339960}, 
    {     0.00000000511,  4.48770393640,    10021.83728009940}, 
    {     0.00000000360,  5.07296615717,      155.42039943420}, 
    {     0.00000000202,  4.88361321440,    13362.44970679920}, 
    {     0.00000000165,  3.48592135141,     3340.61242669980}, 
    {     0.00000000100,  6.09065293613,      242.72860397400}, 
    {     0.00000000062,  5.25625355993,    16703.06213349900}, 
    {     0.00000000064,  1.57192173495,     3185.19202726560}, 
    {     0.00000000035,  3.68331841812,      553.56940284240}, 
    {     0.00000000016,  5.23951751422,     3496.03282613400}, 
    {     0.00000000017,  5.60862454832,    20043.67456019880}, 
    {     0.00000000016,  0.16723854805,     3583.34103067380}, 
    {     0.00000000011,  1.93419597527,     6525.80445396540}, 
    {     0.00000000007,  5.17525588419,     3344.13554504880}, 
    {     0.00000000007,  2.97300501488,     2787.04302385740}, 
    {     0.00000000005,  0.39000584564,     3097.88382272579}, 
    {     0.00000000005,  5.60123387975,     6684.74797174860}, 
    {     0.00000000004,  5.97749583912,    23384.28698689860}, 
    {     0.00000000003,  2.29064254081,     9866.41688066520}, 
    {     0.00000000003,  0.52716684104,     6923.95345737360}, 
    {     0.00000000003,  6.06139189331,    10025.36039844840}, 
    {     0.00000000002,  0.00000000000,        0.00000000000}, 
    {     0.00000000002,  0.06588431932,    26724.89941359840}, 
    {     0.00000000001,  3.33966357719,     6127.65545055720}, 
};


static const struct ln_vsop mars_latitude_b0[LAT_B0] = {
    {     0.03197134986,  3.76832042431,     3340.61242669980}, 
    {     0.00298033234,  4.10616996305,     6681.22485339960}, 
    {     0.00289104742,  0.00000000000,        0.00000000000}, 
    {     0.00031365539,  4.44651053090,    10021.83728009940}, 
    {     0.00003484100,  4.78812549260,    13362.44970679920}, 
    {     0.00000442999,  5.65233014206,     3337.08930835080}, 
    {     0.00000443401,  5.02642622964,     3344.13554504880}, 
    {     0.00000399109,  5.13056816928,    16703.06213349900}, 
    {     0.00000292506,  3.79290674178,     2281.23049651060}, 
    {     0.00000181982,  6.13648041445,     6151.53388830500}, 
    {     0.00000163159,  4.26399640691,      529.69096509460}, 
    {     0.00000159678,  2.23194572851,     1059.38193018920}, 
    {     0.00000139323,  2.41796458896,     8962.45534991020}, 
    {     0.00000149297,  2.16501221175,     5621.84292321040}, 
    {     0.00000142686,  1.18215016908,     3340.59517304760}, 
    {     0.00000142685,  3.21292181638,     3340.62968035200}, 
    {     0.00000082544,  5.36667920373,     6684.74797174860}, 
    {     0.00000073639,  5.09187695770,      398.14900340820}, 
    {     0.00000072660,  5.53775735826,     6283.07584999140}, 
    {     0.00000086377,  5.74429749104,     3738.76143010800}, 
    {     0.00000083276,  5.98866355811,     6677.70173505060}, 
    {     0.00000060116,  3.67960801961,      796.29800681640}, 
    {     0.00000063111,  0.73049101791,     5884.92684658320}, 
    {     0.00000062338,  4.85072128690,     2942.46342329160}, 
    {     0.00000046951,  5.54339769619,     3340.54511639700}, 
    {     0.00000046953,  5.13486674212,     3340.67973700260}, 
    {     0.00000046630,  5.47361589877,    20043.67456019880}, 
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    {     0.00000000112,  0.16839834843,      135.06508003540}, 
    {     0.00000000137,  3.34809361979,     3341.04230982650}, 
    {     0.00000000126,  1.32248977876,     1349.86740965880}, 
    {     0.00000000111,  3.14219193941,    13524.91634293140}, 
    {     0.00000000119,  5.95363422696,    12295.95422960920}, 
    {     0.00000000131,  5.09769592268,    14158.74771361560}, 
    {     0.00000000141,  1.37128440708,     3169.93955608060}, 
    {     0.00000000112,  3.35851628879,     5989.06725217280}, 
    {     0.00000000104,  5.00797771373,    13119.72110282519}, 
    {     0.00000000110,  5.23389059260,     1375.77379984580}, 
    {     0.00000000105,  2.72700704697,     1162.47470440780}, 
    {     0.00000000104,  1.73770183724,     2221.85663459700}, 
    {     0.00000000137,  1.04576950390,     3340.18254357310}, 
    {     0.00000000106,  6.13491390193,      162.46663613220}, 
    {     0.00000000119,  2.63313118842,     7321.12213971360}, 
    {     0.00000000105,  3.09659915297,    20618.01935853360}, 
    {     0.00000000108,  1.01854560270,     3265.83082813250}, 
    {     0.00000000098,  4.23346395354,    23539.70738633280}, 
    {     0.00000000119,  4.07130782746,    10184.30391623160}, 
    {     0.00000000096,  1.81114730032,    10001.06188460700}, 
    {     0.00000000093,  3.58891064965,     5099.26550511660}, 
    {     0.00000000095,  4.94769174828,     3981.49003408200}, 
    {     0.00000000094,  5.37501534644,    13355.33615979840}, 
    {     0.00000000103,  0.43484814704,     1861.74585263540}, 
    {     0.00000000094,  0.13428933842,    15508.61512327440}, 
    {     0.00000000090,  3.76399049820,    22324.90505670940}, 
    {     0.00000000091,  3.95036658260,    10042.61267559180}, 
    {     0.00000000106,  4.30211754376,      640.87760738220}, 
    {     0.00000000109,  6.18873803073,     1478.86657406440}, 
    {     0.00000000088,  1.79608901341,     6247.51311552280}, 
    {     0.00000000102,  5.58780810365,     2766.26762836500}, 
    {     0.00000000110,  0.94707767481,     3274.12501778540}, 
    {     0.00000000084,  4.45487801852,     6696.47732458460}, 
    {     0.00000000085,  2.74791518135,     3407.09983561420}, 
    {     0.00000000087,  4.51187502918,      220.41264243880}, 
    {     0.00000000101,  5.94873233824,     8425.65083781480}, 
    {     0.00000000082,  0.01853826918,     9499.25986200560}, 
    {     0.00000000080,  0.42610497232,    18052.92954315780}, 
    {     0.00000000083,  2.96589752222,     6652.77566593180}, 
    {     0.00000000080,  4.61484797156,     3914.95722503460}, 
    {     0.00000000089,  3.53078320469,     9485.03276800400}, 
    {     0.00000000079,  1.50228054154,     2111.65031337760}, 
    {     0.00000000086,  0.42024324898,      956.28915597060}, 
    {     0.00000000088,  5.46048231018,    16460.33352952499}, 
    {     0.00000000091,  2.09965252231,      949.17560896980}, 
    {     0.00000000104,  1.72206104768,     3296.89351439480}, 
    {     0.00000000103,  1.25691413032,     3384.33133900480}, 
    {     0.00000000084,  5.78633258361,     5518.75014899180}, 
    {     0.00000000079,  1.79312483182,       38.13303563780}, 
    {     0.00000000073,  0.10771411146,    29822.78323632420}, 
    {     0.00000000087,  2.11653872859,     3450.81874791920}, 
    {     0.00000000071,  3.89470981165,     9380.95967271720}, 
    {     0.00000000075,  2.59391377956,     1964.83862685400}, 
    {     0.00000000098,  4.01500805880,     6843.69148953180}, 
    {     0.00000000079,  2.20331656568,    30220.93223973240}, 
    {     0.00000000074,  5.32028984035,    11766.26326451460}, 
    {     0.00000000068,  0.04696396376,     2125.87740737920}, 
    {     0.00000000069,  6.07535832352,    26482.17080962440}, 
    {     0.00000000084,  0.16860055001,      263.08392337280}, 
    {     0.00000000069,  2.05050096393,    29424.63423291600}, 
    {     0.00000000068,  5.03020376497,     9070.11887384880}, 
    {     0.00000000076,  2.00296092459,      224.34479570190}, 
    {     0.00000000066,  3.85497672006,    19406.67828817460}, 
    {     0.00000000066,  5.70059718736,    33561.54466643220}, 
    {     0.00000000067,  0.16590056505,    22743.40937951640}, 
    {     0.00000000065,  4.65403865898,     2807.39834325620}, 
    {     0.00000000069,  3.34398269353,    11670.28403729680}, 
    {     0.00000000087,  4.97795118361,     1118.75579210280}, 
    {     0.00000000063,  0.18907107644,    30065.51184029820}, 
    {     0.00000000064,  4.61910278723,     9886.77220006400}, 
    {     0.00000000073,  0.93704276887,    20735.83216142559}, 
    {     0.00000000060,  5.83782810193,     8646.06348025360}, 
    {     0.00000000062,  4.81385996015,    20199.09495963300}, 
    {     0.00000000059,  5.00167022948,     6414.61781167780}, 
    {     0.00000000068,  3.84295373259,     6571.01853218020}, 
    {     0.00000000061,  2.81706693695,     6944.30877677240}, 
    {     0.00000000065,  4.49019257083,      632.78373931320}, 
    {     0.00000000058,  5.65218977997,     9945.57120882380}, 
    {     0.00000000071,  2.51550158926,     9638.94074787620}, 
    {     0.00000000057,  3.27978831470,      206.18554843720}, 
    {     0.00000000058,  2.97636193658,    21795.21409161479}, 
    {     0.00000000056,  2.23539566426,    20995.39296644940}, 
    {     0.00000000057,  1.88470380043,    18451.07854656599}, 
    {     0.00000000071,  4.82445654330,     8542.97070603500}, 
    {     0.00000000061,  3.65964735564,    14421.83163698840}, 
    {     0.00000000056,  3.13785930666,     8799.98871377800}, 
    {     0.00000000057,  4.89910616374,     9602.35263622420}, 
    {     0.00000000065,  3.37158994673,    11610.91017538320}, 
    {     0.00000000067,  1.92961865108,    21265.52312652020}, 
    {     0.00000000055,  1.95164531766,     9588.12554222260}, 
    {     0.00000000057,  2.82246123078,    10124.93005431800}, 
    {     0.00000000057,  6.10387785338,    19800.94595622480}, 
    {     0.00000000055,  5.20958408712,     3237.51965248120}, 
    {     0.00000000057,  4.12311973381,    10028.95082710020}, 
    {     0.00000000054,  1.41693548950,    15906.76412668260}, 
    {     0.00000000053,  2.16367301961,     6418.14093002680}, 
    {     0.00000000060,  2.64664637730,    10018.24685144760}, 
    {     0.00000000068,  5.36545296940,     1228.96211332220}, 
    {     0.00000000051,  5.73844646896,     6048.44111408640}, 
    {     0.00000000053,  0.32024828883,    12721.57209941700}, 
    {     0.00000000051,  0.06318823307,    20206.14119633100}, 
    {     0.00000000049,  4.53400634462,     6675.70192909220}, 
    {     0.00000000051,  1.15453549218,    10156.90236013480}, 
    {     0.00000000064,  4.56324217308,    16703.07938715119}, 
    {     0.00000000060,  3.61007876606,     9468.26787725700}, 
    {     0.00000000059,  3.08394474122,    10025.42770875120}, 
    {     0.00000000064,  2.53221459501,    16703.04487984680}, 
    {     0.00000000056,  3.31981662811,     6518.75821726740}, 
    {     0.00000000047,  1.44559124267,     6643.09181776180}, 
    {     0.00000000050,  1.92346411481,    11614.43329373220}, 
    {     0.00000000047,  4.03823773711,    23958.63178523340}, 
    {     0.00000000046,  3.70969689047,     8859.36257569160}, 
    {     0.00000000060,  2.55451756882,    11780.49035851620}, 
    {     0.00000000047,  1.69255946598,     6660.86953400080}, 
    {     0.00000000044,  6.09481156053,     6460.81221096080}, 
    {     0.00000000044,  2.63075457414,    13936.79450513400}, 
    {     0.00000000053,  0.77837832855,    16865.52876963120}, 
    {     0.00000000049,  1.83317426993,    17654.78053974960}, 
    {     0.00000000042,  4.30403794400,     9065.54812412880}, 
    {     0.00000000047,  0.52827244925,     6686.74777770700}, 
    {     0.00000000042,  5.72053684220,     7203.80227149340}, 
    {     0.00000000041,  0.98430028881,    20426.57109242200}, 
    {     0.00000000051,  3.54371303345,    20597.24396304120}, 
    {     0.00000000041,  0.21190431801,     7314.00859271280}, 
    {     0.00000000038,  2.53053802253,    13207.02930736500}, 
    {     0.00000000039,  5.15577529354,     6670.58818804980}, 
    {     0.00000000045,  0.52366150729,    16489.76303806100}, 
    {     0.00000000051,  3.25181148972,     7799.98064550240}, 
    {     0.00000000049,  0.77149145450,    17101.21113690720}, 
    {     0.00000000038,  6.06656444914,     9389.05354078620}, 
    {     0.00000000036,  0.84094545235,    23937.85638974100}, 
};


static const struct ln_vsop mars_latitude_b1[LAT_B1] = {
    {     0.00217310991,  6.04472194776,     3340.61242669980}, 
    {     0.00020976948,  3.14159265359,        0.00000000000}, 
    {     0.00012834709,  1.60810667915,     6681.22485339960}, 
    {     0.00003320981,  2.62947004077,    10021.83728009940}, 
    {     0.00000627200,  3.11898601248,    13362.44970679920}, 
    {     0.00000101990,  3.52113557592,    16703.06213349900}, 
    {     0.00000075107,  0.95983758515,     3337.08930835080}, 
    {     0.00000029264,  3.40307682710,     3344.13554504880}, 
    {     0.00000023251,  3.69342549027,     5621.84292321040}, 
    {     0.00000022190,  2.21703408598,     2281.23049651060}, 
    {     0.00000015454,  3.89610159362,    20043.67456019880}, 
    {     0.00000011867,  3.83861019788,     6684.74797174860}, 
    {     0.00000012038,  2.13866775328,     6151.53388830500}, 
    {     0.00000009697,  5.48941186798,     3340.62968035200}, 
    {     0.00000009697,  3.45863925102,     3340.59517304760}, 
    {     0.00000011537,  1.90395033905,     3532.06069281140}, 
    {     0.00000009276,  0.71941312462,     2942.46342329160}, 
    {     0.00000009240,  2.51747952408,     5884.92684658320}, 
    {     0.00000009876,  6.13507416822,     1059.38193018920}, 
    {     0.00000009265,  4.55759125226,     8962.45534991020}, 
    {     0.00000007822,  6.10932267009,     2810.92146160520}, 
    {     0.00000010369,  0.60195347181,      529.69096509460}, 
    {     0.00000008522,  4.40106741096,     3496.03282613400}, 
    {     0.00000007683,  1.21169696624,     6677.70173505060}, 
    {     0.00000007134,  1.93610705535,     2544.31441988340}, 
    {     0.00000006512,  3.11636422105,     3738.76143010800}, 
    {     0.00000006278,  6.23176923902,     3185.19202726560}, 
    {     0.00000005833,  0.74324094343,      398.14900340820}, 
    {     0.00000005033,  2.28727456802,     3149.16416058820}, 
    {     0.00000004958,  1.54200127913,     6283.07584999140}, 
    {     0.00000004325,  3.90636722132,     5092.15195811580}, 
    {     0.00000004813,  3.88560399245,     5486.77784317500}, 
    {     0.00000004474,  2.18937641288,     4136.91043351620}, 
    {     0.00000003023,  5.19879000530,     5088.62883976680}, 
    {     0.00000003194,  1.12695072198,     3340.67973700260}, 
    {     0.00000003167,  0.76774265684,     4399.99435688900}, 
    {     0.00000003066,  0.93923788410,     2914.01423582380}, 
    {     0.00000002840,  2.51888046278,     3870.30339179440}, 
    {     0.00000002622,  3.25368667606,     3339.63210563160}, 
    {     0.00000003192,  1.53317813619,     3340.54511639700}, 
    {     0.00000002879,  4.20588113950,    10025.36039844840}, 
    {     0.00000002435,  2.49243229030,     1751.53953141600}, 
    {     0.00000002066,  2.96021692416,     3894.18182954220}, 
    {     0.00000002366,  1.08506560814,      796.29800681640}, 
    {     0.00000002192,  0.22905210418,     4690.47983635860}, 
    {     0.00000002398,  0.43514026515,     1194.44701022460}, 
    {     0.00000002238,  4.06454135883,     7079.37385680780}, 
    {     0.00000001825,  5.46319390380,     1592.59601363280}, 
    {     0.00000001808,  4.83342714362,     8432.76438481560}, 
    {     0.00000002251,  4.25857270742,    23384.28698689860}, 
    {     0.00000001728,  1.06103820676,     3341.59274776800}, 
    {     0.00000001833,  1.57091276737,     4292.33083295040}, 
    {     0.00000001581,  0.93404031162,     4535.05943692440}, 
    {     0.00000001722,  2.98790749378,     6254.62666252360}, 
    {     0.00000001395,  3.43004445438,     2146.16541647520}, 
    {     0.00000001739,  4.00666290186,     9492.14631500480}, 
    {     0.00000001535,  2.94481028624,     6489.77658728800}, 
    {     0.00000001394,  2.71952784799,     7477.52286021600}, 
    {     0.00000001257,  1.34371702718,     2787.04302385740}, 
    {     0.00000001600,  5.41971849753,     3127.31333126180}, 
    {     0.00000001274,  4.11492658217,     1990.74501704100}, 
    {     0.00000001190,  4.24621398204,     3723.50895892300}, 
    {     0.00000001144,  5.30298760566,     6681.20759974740}, 
    {     0.00000001376,  0.38090537503,     1589.07289528380}, 
    {     0.00000001144,  1.05059380873,     6681.24210705180}, 
    {     0.00000001062,  0.51072898484,     6674.11130639880}, 
    {     0.00000001355,  0.30172057784,     6525.80445396540}, 
    {     0.00000001119,  0.28227067739,    12303.06777661000}, 
    {     0.00000000855,  0.15965897606,     2957.71589447660}, 
    {     0.00000001066,  2.74229978174,     2388.89402044920}, 
    {     0.00000001056,  4.82485604808,     3583.34103067380}, 
    {     0.00000000770,  3.92387598679,        7.11354700080}, 
    {     0.00000000922,  5.97832717399,     3097.88382272579}, 
    {     0.00000000713,  2.61601602080,     9225.53927328300}, 
    {     0.00000000693,  5.86945792010,     4933.20844033260}, 
    {     0.00000000738,  5.02837731897,    12832.75874170460}, 
    {     0.00000000763,  1.29638960572,     7740.60678358880}, 
    {     0.00000000656,  1.57943668761,     6467.92575796160}, 
    {     0.00000000663,  0.56970117211,      426.59819087600}, 
    {     0.00000000616,  2.90595542135,     3553.91152213780}, 
    {     0.00000000609,  4.27586920886,     4562.46099302120}, 
    {     0.00000000608,  4.61163488420,    10419.98628350760}, 
    {     0.00000000599,  4.51624214272,     6836.64525283380}, 
    {     0.00000000565,  3.63229110969,      155.42039943420}, 
    {     0.00000000562,  0.31418284081,      213.29909543800}, 
    {     0.00000000519,  1.00557611591,     4929.68532198360}, 
    {     0.00000000504,  4.17532879019,     6041.32756708560}, 
    {     0.00000000660,  3.62669217851,     7210.91581849420}, 
    {     0.00000000576,  4.54911948486,    13365.97282514820}, 
    {     0.00000000625,  1.44798343162,     3333.49887969900}, 
    {     0.00000000520,  1.30331504622,    15643.68020330980}, 
    {     0.00000000444,  2.08076069460,    10021.85453375160}, 
    {     0.00000000542,  2.02587783935,     2288.34404351140}, 
    {     0.00000000509,  1.65323927554,      191.44826611160}, 
    {     0.00000000444,  0.04999320087,    10021.82002644720}, 
    {     0.00000000557,  3.31349841992,     9623.68827669120}, 
    {     0.00000000472,  6.26731124720,     6438.49624942560}, 
    {     0.00000000559,  4.16781257217,    11773.37681151540}, 
    {     0.00000000399,  1.32358791559,     7875.67186362420}, 
    {     0.00000000445,  1.49656750781,     6682.20517446780}, 
    {     0.00000000385,  0.75203057166,     5614.72937620960}, 
    {     0.00000000386,  1.92088879703,     3325.35995551480}, 
    {     0.00000000377,  3.38213849272,     6681.15754309680}, 
    {     0.00000000360,  3.62049849377,     6680.24453233140}, 
    {     0.00000000352,  3.40685833182,     9830.38901398780}, 
    {     0.00000000346,  2.54878403272,     2274.11694950980}, 
    {     0.00000000336,  5.51924409428,     3361.38782219220}, 
    {     0.00000000329,  3.58450091417,     1066.49547719000}, 
    {     0.00000000343,  3.80876454378,     9595.23908922340}, 
    {     0.00000000383,  4.58860426691,     3360.96774609859}, 
    {     0.00000000367,  4.94614944232,     7903.07341972100}, 
    {     0.00000000318,  3.12211289329,    10818.13528691580}, 
    {     0.00000000298,  5.16474580641,     1748.01641306700}, 
    {     0.00000000310,  5.77231072116,     3205.54734666440}, 
    {     0.00000000378,  2.97214989967,     6681.29216370240}, 
    {     0.00000000303,  3.44801982034,     3319.83703120740}, 
    {     0.00000000292,  1.69888047283,     6127.65545055720}, 
    {     0.00000000288,  1.13506530643,     8955.34180290940}, 
    {     0.00000000281,  0.80027819229,    10018.31416175040}, 
    {     0.00000000326,  5.96924076920,      639.89728631400}, 
    {     0.00000000309,  1.38061994912,     3767.21061757580}, 
    {     0.00000000375,  4.48892934736,     5331.35744374080}, 
    {     0.00000000271,  4.61196466416,    26724.89941359840}, 
    {     0.00000000266,  3.08927427780,     5729.50644714900}, 
    {     0.00000000290,  2.44792712887,     3355.86489788480}, 
    {     0.00000000335,  6.08508450491,     3320.25710730100}, 
    {     0.00000000300,  0.25476556615,     2700.71514038580}, 
    {     0.00000000289,  3.45335160291,      382.89653222320}, 
    {     0.00000000260,  3.56570589402,     8827.39026987480}, 
    {     0.00000000246,  0.64772929845,     9866.41688066520}, 
    {     0.00000000298,  4.38515379625,     1052.26838318840}, 
    {     0.00000000251,  4.40903417777,    12964.30070339100}, 
    {     0.00000000260,  1.27300653213,     3347.72597370060}, 
    {     0.00000000280,  1.49182583330,    10213.28554621100}, 
    {     0.00000000225,  2.73440886519,     6872.67311951120}, 
    {     0.00000000225,  5.16642343920,     6923.95345737360}, 
    {     0.00000000226,  2.68107364511,     1221.84856632140}, 
    {     0.00000000222,  4.38874821491,      242.72860397400}, 
    {     0.00000000209,  5.01591708290,     6144.42034130420}, 
    {     0.00000000268,  2.27786943096,      553.56940284240}, 
    {     0.00000000218,  0.53299582810,     6298.32832117640}, 
    {     0.00000000261,  3.89759063291,     6894.52394883760}, 
    {     0.00000000213,  1.06038488787,     2118.76386037840}, 
    {     0.00000000210,  4.74220753176,     9381.93999378540}, 
    {     0.00000000192,  0.18364684632,      522.57741809380}, 
    {     0.00000000186,  1.48154759746,     7064.12138562280}, 
    {     0.00000000176,  3.93023367762,     2921.12778282460}, 
    {     0.00000000208,  4.86366921136,     3344.20285535160}, 
    {     0.00000000201,  0.36731227894,     8969.56889691100}, 
    {     0.00000000209,  4.43309730358,     3337.02199804800}, 
    {     0.00000000163,  4.54501296893,    11243.68584642080}, 
    {     0.00000000161,  1.62341728854,    11081.21921028860}, 
    {     0.00000000152,  3.98251813705,    10021.90459040220}, 
    {     0.00000000145,  1.06283180181,      951.71840625060}, 
    {     0.00000000149,  4.55824612447,    10551.52824519400}, 
    {     0.00000000184,  5.37374692745,    16173.37116840440}, 
    {     0.00000000143,  2.00077774476,     6688.33840040040}, 
    {     0.00000000145,  4.53139041634,     3312.16323923200}, 
    {     0.00000000156,  6.26070301430,     5628.95647021120}, 
    {     0.00000000157,  5.56167088817,      536.80451209540}, 
    {     0.00000000133,  5.43195789258,    13358.92658845020}, 
    {     0.00000000144,  1.31943624453,     3364.49086444760}, 
    {     0.00000000156,  4.10544868136,     6158.64743530580}, 
    {     0.00000000157,  6.23025291402,     8273.82086703240}, 
    {     0.00000000134,  4.31700501659,     8031.09226305840}, 
    {     0.00000000124,  1.26816196203,     8270.29774868340}, 
    {     0.00000000156,  4.39354558071,    10021.76996979660}, 
    {     0.00000000144,  2.48806691402,     3503.07906283200}, 
    {     0.00000000118,  1.78550823737,    18984.29263000960}, 
    {     0.00000000110,  6.12714281903,     7632.94325965020}, 
    {     0.00000000127,  3.05541911618,     3316.73398895200}, 
    {     0.00000000109,  0.91919644775,    10014.72373309860}, 
    {     0.00000000102,  1.54908471746,     7234.79425624200}, 
    {     0.00000000100,  5.04817125533,    13760.59871020740}, 
    {     0.00000000132,  2.66590263580,     8429.24126646660}, 
    {     0.00000000126,  0.13960736597,     1349.86740965880}, 
    {     0.00000000100,  0.74385347353,     2487.41604494780}, 
    {     0.00000000091,  0.24627212892,     3980.50971301380}, 
    {     0.00000000112,  2.30475590800,     3346.13535100720}, 
    {     0.00000000103,  4.23425277305,     3475.67750673520}, 
    {     0.00000000109,  3.21402242606,    17654.78053974960}, 
    {     0.00000000082,  0.28323060532,    15113.98923821520}, 
    {     0.00000000083,  0.53618493739,    13362.43245314700}, 
    {     0.00000000096,  3.66896983898,    12168.00269657460}, 
    {     0.00000000083,  2.56708795058,    13362.46696045140}, 
    {     0.00000000077,  4.92321070753,    16706.58525184800}, 
    {     0.00000000097,  2.11149094902,     3178.14579056760}, 
    {     0.00000000074,  0.95663828948,     2699.73481931760}, 
    {     0.00000000083,  1.82502676147,        3.52311834900}, 
    {     0.00000000085,  5.22946780555,     3304.58456002240}, 
    {     0.00000000083,  3.10647417000,     1758.65307841680}, 
    {     0.00000000070,  5.11510436801,     5828.02847164760}, 
    {     0.00000000077,  1.77323016185,     3335.08950239240}, 
    {     0.00000000082,  5.25824044848,      853.19638175200}, 
    {     0.00000000067,  0.98915661779,      433.71173787680}, 
    {     0.00000000078,  3.62913840245,     1596.18644228460}, 
    {     0.00000000078,  1.56367501585,     3336.73109134180}, 
    {     0.00000000084,  4.62334317796,    11371.70468975820}, 
    {     0.00000000072,  3.62008128206,     1581.95934828300}, 
    {     0.00000000072,  4.05769658716,     4407.10790388980}, 
    {     0.00000000085,  0.75421401009,     5459.37628707820}, 
    {     0.00000000074,  1.03163916867,     5085.03841111500}, 
    {     0.00000000058,  3.24082931383,    13517.87010623340}, 
    {     0.00000000056,  3.73441989631,    10713.99488132620}, 
    {     0.00000000061,  1.52242466354,    18052.92954315780}, 
    {     0.00000000053,  0.69821482369,     6702.00024889200}, 
    {     0.00000000057,  2.76439103910,     3344.49376205780}, 
    {     0.00000000069,  1.99074407937,    10575.40668294180}, 
    {     0.00000000059,  1.90513947603,    10022.81760116760}, 
    {     0.00000000051,  0.93662679832,    14314.16811304980}, 
    {     0.00000000069,  5.42699929964,     3376.64029337720}, 
    {     0.00000000053,  4.87818342068,     8671.96987044060}, 
    {     0.00000000065,  3.39290651505,    14584.29827312060}, 
    {     0.00000000057,  1.70570965163,     2648.45482547300}, 
    {     0.00000000054,  5.49765437527,     3369.06161416760}, 
    {     0.00000000054,  2.28971906454,    12566.15169998280}, 
    {     0.00000000068,  4.60849144076,     7373.38245462640}, 
    {     0.00000000049,  2.89959771413,    13916.01910964160}, 
    {     0.00000000058,  4.18351190862,    10177.25767953360}, 
    {     0.00000000058,  4.51310742397,     4032.77002792660}, 
    {     0.00000000048,  3.42793333559,     1744.42598441520}, 
    {     0.00000000064,  0.45002982477,     3863.18984479360}, 
    {     0.00000000047,  5.88584556234,    10973.55568635000}, 
    {     0.00000000057,  1.76184909465,    11216.28429032400}, 
    {     0.00000000053,  1.35755250698,    21393.54196985760}, 
    {     0.00000000059,  2.91197893810,     3981.49003408200}, 
    {     0.00000000053,  4.03461050047,    11769.85369316640}, 
    {     0.00000000052,  2.05672710904,    10404.73381232260}, 
    {     0.00000000060,  4.31863902545,     3077.52850332700}, 
    {     0.00000000060,  4.94577585891,     3603.69635007260}, 
    {     0.00000000052,  3.45056061273,     9808.53818466140}, 
    {     0.00000000048,  3.83792333621,    13171.00144068760}, 
    {     0.00000000050,  1.55014152662,      419.48464387520}, 
    {     0.00000000042,  1.56007012481,     8425.65083781480}, 
    {     0.00000000040,  4.52149159432,    10235.13637553740}, 
    {     0.00000000045,  4.94000875201,    16304.91313009080}, 
    {     0.00000000042,  2.03301048111,     7107.82304427560}, 
    {     0.00000000055,  2.94325348897,      640.87760738220}, 
    {     0.00000000039,  0.82091082076,    12310.18132361080}, 
    {     0.00000000040,  3.29013672690,     6247.51311552280}, 
    {     0.00000000040,  0.33830589904,     6531.66165626500}, 
    {     0.00000000044,  4.73395183232,    20597.24396304120}, 
    {     0.00000000037,  0.01359265708,     3914.95722503460}, 
    {     0.00000000037,  3.04848190227,     2766.26762836500}, 
    {     0.00000000037,  4.13243009725,    17256.63153634140}, 
    {     0.00000000043,  3.27442666790,    20995.39296644940}, 
    {     0.00000000035,  0.29856523330,     9779.10867612540}, 
    {     0.00000000045,  0.96453304167,    18454.60166491500}, 
    {     0.00000000036,  0.18334758502,     6660.86953400080}, 
    {     0.00000000043,  1.23912278835,     8439.87793181640}, 
    {     0.00000000034,  2.83078633705,     6696.47732458460}, 
    {     0.00000000043,  5.80649509131,     9168.64089834740}, 
    {     0.00000000034,  3.46884113350,     9070.11887384880}, 
    {     0.00000000037,  5.04438408684,     1692.16566950240}, 
    {     0.00000000040,  1.15262282119,    14712.31711645800}, 
    {     0.00000000035,  2.33581709312,       76.26607127560}, 
    {     0.00000000040,  3.54052855946,    14158.74771361560}, 
    {     0.00000000032,  4.96078703650,    24734.15439655740}, 
    {     0.00000000029,  2.34589185801,    13745.34623902240}, 
    {     0.00000000030,  6.17825920695,    12935.85151592320}, 
    {     0.00000000036,  4.78354946118,     3191.04922956520}, 
    {     0.00000000028,  4.98887480054,    30065.51184029820}, 
    {     0.00000000028,  2.51507274088,      692.15760122680}, 
    {     0.00000000027,  1.02364014288,    13207.02930736500}, 
    {     0.00000000035,  2.06348913435,     9468.26787725700}, 
    {     0.00000000027,  6.07463404086,    20199.09495963300}, 
    {     0.00000000027,  4.97808057680,    13362.38239649640}, 
    {     0.00000000033,  1.46173724832,    12295.95422960920}, 
    {     0.00000000025,  4.54782445360,     9499.25986200560}, 
    {     0.00000000025,  5.21847833578,     5099.26550511660}, 
    {     0.00000000025,  5.90368432966,    19513.98359510420}, 
    {     0.00000000025,  5.54544644558,    10264.56588407340}, 
    {     0.00000000029,  5.69085985167,    16699.53901514999}, 
    {     0.00000000030,  1.43603228163,     6040.34724601740}, 
    {     0.00000000028,  5.41811683281,    15110.46611986620}, 
    {     0.00000000032,  2.25828272513,     6665.97238221460}, 
    {     0.00000000023,  5.38626329146,     6660.44945790720}, 
    {     0.00000000023,  3.75194149686,    14054.60730802600}, 
    {     0.00000000028,  4.86716760481,     6701.58017279840}, 
    {     0.00000000027,  5.26172837256,     6816.28993343500}, 
    {     0.00000000023,  4.66125245752,    13149.15061136120}, 
    {     0.00000000027,  0.91821785260,     9638.94074787620}, 
    {     0.00000000023,  0.60587177409,     6604.95878212400}, 
    {     0.00000000025,  0.78041098485,    11766.26326451460}, 
    {     0.00000000025,  3.94777048397,    10020.85695903120}, 
    {     0.00000000026,  5.36280311705,     9485.03276800400}, 
    {     0.00000000020,  2.45752476953,    10028.95082710020}, 
    {     0.00000000020,  0.38029885589,    11614.43329373220}, 
    {     0.00000000026,  4.53241539149,    13362.51701710200}, 
    {     0.00000000019,  3.71366407424,     9588.12554222260}, 
    {     0.00000000022,  5.20856925736,    13892.14067189380}, 
};


static const struct ln_vsop mars_latitude_b2[LAT_B2] = {
    {     0.00008888446,  1.06196052751,     3340.61242669980}, 
    {     0.00002595393,  3.14159265359,        0.00000000000}, 
    {     0.00000918914,  0.11538431190,     6681.22485339960}, 
    {     0.00000267883,  0.78837893063,    10021.83728009940}, 
    {     0.00000066911,  1.39435595847,    13362.44970679920}, 
    {     0.00000014267,  1.87268116087,    16703.06213349900}, 
    {     0.00000007948,  2.58819177832,     3337.08930835080}, 
    {     0.00000002709,  2.29241371893,    20043.67456019880}, 
    {     0.00000002911,  1.36634316448,     3344.13554504880}, 
    {     0.00000002528,  6.00423798411,     3496.03282613400}, 
    {     0.00000001617,  5.72212771018,     5621.84292321040}, 
    {     0.00000001625,  4.63140305669,     3185.19202726560}, 
    {     0.00000001173,  2.04871812080,     6684.74797174860}, 
    {     0.00000001066,  1.15825195582,     2281.23049651060}, 
    {     0.00000001043,  3.54796199484,     3532.06069281140}, 
    {     0.00000000724,  4.20458660775,     5884.92684658320}, 
    {     0.00000000610,  5.22430575829,     2810.92146160520}, 
    {     0.00000000557,  2.75698163218,     2942.46342329160}, 
    {     0.00000000655,  2.84033212598,     6677.70173505060}, 
    {     0.00000000641,  5.44557723446,     5486.77784317500}, 
    {     0.00000000498,  4.59850630546,     3894.18182954220}, 
    {     0.00000000501,  0.52535712881,     5088.62883976680}, 
    {     0.00000000521,  4.66308888977,     1059.38193018920}, 
    {     0.00000000490,  3.99314993252,     2544.31441988340}, 
    {     0.00000000408,  4.93937427401,     3339.63210563160}, 
    {     0.00000000396,  0.51430149629,     3340.62968035200}, 
    {     0.00000000470,  2.68379670864,    23384.28698689860}, 
    {     0.00000000389,  6.00426372731,     8962.45534991020}, 
    {     0.00000000446,  3.81307040390,     6151.53388830500}, 
    {     0.00000000396,  4.76665218791,     3340.59517304760}, 
    {     0.00000000360,  0.30420986478,     4136.91043351620}, 
    {     0.00000000368,  2.55488502496,    10025.36039844840}, 
    {     0.00000000417,  2.05816647037,      529.69096509460}, 
    {     0.00000000393,  1.18623350431,     3097.88382272579}, 
    {     0.00000000318,  4.89083986180,     5092.15195811580}, 
    {     0.00000000311,  0.52479429819,     3149.16416058820}, 
    {     0.00000000339,  1.91330658550,     4690.47983635860}, 
    {     0.00000000351,  3.22939666067,     4292.33083295040}, 
    {     0.00000000400,  4.99682542425,     6525.80445396540}, 
    {     0.00000000269,  5.24048656863,     4399.99435688900}, 
    {     0.00000000269,  6.01045237753,     2787.04302385740}, 
    {     0.00000000242,  5.84228858137,     3723.50895892300}, 
    {     0.00000000300,  3.33780918870,     3583.34103067380}, 
    {     0.00000000230,  1.39226657786,     3738.76143010800}, 
    {     0.00000000192,  5.54090794612,     3341.59274776800}, 
    {     0.00000000185,  2.67271130688,     6283.07584999140}, 
    {     0.00000000184,  2.21130914624,     7079.37385680780}, 
    {     0.00000000170,  5.17306622171,     6254.62666252360}, 
    {     0.00000000186,  3.68212348930,     1592.59601363280}, 
    {     0.00000000168,  2.39044142684,     1990.74501704100}, 
    {     0.00000000201,  0.91789291159,     2388.89402044920}, 
    {     0.00000000171,  4.81773821378,     1194.44701022460}, 
    {     0.00000000181,  2.50145688400,      398.14900340820}, 
    {     0.00000000177,  5.42788143021,     4535.05943692440}, 
    {     0.00000000153,  5.20921140136,     2146.16541647520}, 
    {     0.00000000131,  2.41348963069,     3340.67973700260}, 
    {     0.00000000150,  1.54231915192,     6438.49624942560}, 
    {     0.00000000149,  0.96225780576,     7477.52286021600}, 
    {     0.00000000129,  5.26033357561,      155.42039943420}, 
    {     0.00000000158,  4.47988793489,     3333.49887969900}, 
    {     0.00000000133,  6.05902381899,     6836.64525283380}, 
    {     0.00000000120,  4.73910738283,     2957.71589447660}, 
    {     0.00000000117,  2.22260771124,     6674.11130639880}, 
    {     0.00000000136,  5.83288551607,      796.29800681640}, 
    {     0.00000000157,  1.15241959296,     6489.77658728800}, 
    {     0.00000000110,  4.19180987487,     4933.20844033260}, 
    {     0.00000000130,  2.84683198305,     3340.54511639700}, 
    {     0.00000000121,  2.52786285342,     9492.14631500480}, 
    {     0.00000000108,  0.08979902661,     1748.01641306700}, 
    {     0.00000000117,  5.82410316896,     2914.01423582380}, 
    {     0.00000000086,  2.01927297840,        7.11354700080}, 
    {     0.00000000082,  3.80856644509,     6681.20759974740}, 
    {     0.00000000082,  5.83941329915,     6681.24210705180}, 
    {     0.00000000076,  0.08262821070,     6127.65545055720}, 
    {     0.00000000091,  2.96288127149,    13365.97282514820}, 
    {     0.00000000080,  2.85318684748,     8955.34180290940}, 
    {     0.00000000083,  5.02941237478,    12303.06777661000}, 
    {     0.00000000074,  3.62624366705,     6923.95345737360}, 
    {     0.00000000072,  1.17271788888,     3127.31333126180}, 
    {     0.00000000095,  4.98093994365,     1589.07289528380}, 
    {     0.00000000087,  5.81716080338,     7740.60678358880}, 
    {     0.00000000089,  0.48604673074,     3870.30339179440}, 
    {     0.00000000066,  3.06598137329,    26724.89941359840}, 
    {     0.00000000067,  6.01736846209,     6682.20517446780}, 
    {     0.00000000070,  0.64135636261,     2288.34404351140}, 
    {     0.00000000063,  3.19176567675,    12832.75874170460}, 
    {     0.00000000063,  2.70869032431,      242.72860397400}, 
    {     0.00000000062,  5.92753482553,     7875.67186362420}, 
    {     0.00000000074,  5.12213534011,     9866.41688066520}, 
    {     0.00000000076,  2.80770234482,     5331.35744374080}, 
    {     0.00000000063,  1.40446619803,     5729.50644714900}, 
    {     0.00000000065,  1.35907629616,     1349.86740965880}, 
    {     0.00000000056,  2.65764515134,      951.71840625060}, 
    {     0.00000000067,  4.84212554978,     2274.11694950980}, 
    {     0.00000000069,  2.48893325965,    10419.98628350760}, 
    {     0.00000000051,  5.98407977888,     6041.32756708560}, 
    {     0.00000000049,  4.85570926461,     4562.46099302120}, 
    {     0.00000000058,  4.99207597345,     8969.56889691100}, 
    {     0.00000000043,  5.63823020899,     4929.68532198360}, 
    {     0.00000000058,  6.20594898525,     3347.72597370060}, 
    {     0.00000000057,  2.89730834453,    10018.31416175040}, 
    {     0.00000000058,  3.89480774042,      553.56940284240}, 
    {     0.00000000047,  5.12333023108,      426.59819087600}, 
    {     0.00000000042,  1.03283454214,     6681.29216370240}, 
    {     0.00000000051,  1.17739312127,     1751.53953141600}, 
    {     0.00000000036,  4.71576514590,     6298.32832117640}, 
    {     0.00000000041,  4.11801359055,    10021.82002644720}, 
    {     0.00000000036,  2.79629985388,      213.29909543800}, 
    {     0.00000000033,  5.67092277262,    15643.68020330980}, 
    {     0.00000000033,  1.68550281175,     9830.38901398780}, 
    {     0.00000000032,  2.78277698783,     7210.91581849420}, 
    {     0.00000000041,  6.14975635778,    10021.85453375160}, 
    {     0.00000000031,  1.46914313245,    10818.13528691580}, 
    {     0.00000000030,  5.11654548214,    11773.37681151540}, 
    {     0.00000000030,  5.94013525093,     3767.21061757580}, 
    {     0.00000000028,  1.35093398031,     3553.91152213780}, 
    {     0.00000000027,  0.84036429724,     7632.94325965020}, 
    {     0.00000000029,  5.76529104850,     8031.09226305840}, 
    {     0.00000000026,  0.25856730853,     1066.49547719000}, 
    {     0.00000000024,  0.67405360149,     3360.96774609859}, 
    {     0.00000000024,  2.34265028137,     3320.25710730100}, 
    {     0.00000000028,  1.81680368660,     9623.68827669120}, 
    {     0.00000000022,  6.24243881749,     8432.76438481560}, 
    {     0.00000000021,  5.25722436514,     6680.24453233140}, 
    {     0.00000000023,  4.24982817116,     3325.35995551480}, 
    {     0.00000000022,  5.05378057964,     3355.86489788480}, 
    {     0.00000000026,  5.21495958693,      382.89653222320}, 
    {     0.00000000023,  2.27453854146,     7234.79425624200}, 
    {     0.00000000025,  1.69816682992,     6872.67311951120}, 
    {     0.00000000023,  4.13297133971,      639.89728631400}, 
    {     0.00000000019,  4.63736307953,     8429.24126646660}, 
    {     0.00000000018,  0.29318941103,      640.87760738220}, 
    {     0.00000000017,  3.12909635955,     6467.92575796160}, 
    {     0.00000000016,  1.92178558286,     6681.15754309680}, 
    {     0.00000000016,  0.47472874553,     1052.26838318840}, 
    {     0.00000000016,  0.09800770199,    11081.21921028860}, 
    {     0.00000000018,  3.26217306584,     7064.12138562280}, 
    {     0.00000000016,  5.48746970528,     9595.23908922340}, 
    {     0.00000000019,  4.63958564261,     8273.82086703240}, 
    {     0.00000000015,  2.52623641715,      191.44826611160}, 
    {     0.00000000016,  1.95271387752,     2699.73481931760}, 
    {     0.00000000015,  4.31015619343,     8827.39026987480}, 
    {     0.00000000014,  1.08241159656,    10973.55568635000}, 
    {     0.00000000015,  6.00000660183,    11371.70468975820}, 
    {     0.00000000013,  0.22518942674,     6688.33840040040}, 
    {     0.00000000013,  2.42192861366,    10575.40668294180}, 
    {     0.00000000011,  2.53752217003,    12964.30070339100}, 
    {     0.00000000011,  4.80028625279,    11769.85369316640}, 
    {     0.00000000014,  3.84407896636,    16173.37116840440}, 
    {     0.00000000011,  1.79883656022,     9779.10867612540}, 
    {     0.00000000010,  3.38769942924,    16706.58525184800}, 
    {     0.00000000013,  2.15740232885,     6894.52394883760}, 
    {     0.00000000010,  5.38827104551,    12310.18132361080}, 
    {     0.00000000012,  3.76810144879,     9225.53927328300}, 
    {     0.00000000011,  3.25290731199,     8671.96987044060}, 
    {     0.00000000011,  2.90564118820,     6040.34724601740}, 
    {     0.00000000010,  5.69430086859,    13207.02930736500}, 
    {     0.00000000009,  3.26007781906,    13760.59871020740}, 
    {     0.00000000009,  2.65306894671,    10551.52824519400}, 
    {     0.00000000009,  1.95264065659,     9070.11887384880}, 
    {     0.00000000011,  0.42402934223,     9381.93999378540}, 
};


static const struct ln_vsop mars_latitude_b3[LAT_B3] = {
    {     0.00000330418,  2.04215300484,     3340.61242669980}, 
    {     0.00000093057,  0.00000000000,        0.00000000000}, 
    {     0.00000014546,  5.38525967237,    10021.83728009940}, 
    {     0.00000008731,  4.90252313032,     6681.22485339960}, 
    {     0.00000005215,  5.97441462813,    13362.44970679920}, 
    {     0.00000001422,  0.21283650226,    16703.06213349900}, 
    {     0.00000000585,  4.14327356645,     3337.08930835080}, 
    {     0.00000000489,  1.32053432093,     3496.03282613400}, 
    {     0.00000000332,  0.67062028539,    20043.67456019880}, 
    {     0.00000000281,  3.02888736938,     3185.19202726560}, 
    {     0.00000000095,  0.68129190368,     5621.84292321040}, 
    {     0.00000000117,  6.20178829761,     3344.13554504880}, 
    {     0.00000000100,  2.70816972496,     3097.88382272579}, 
    {     0.00000000086,  0.38064581922,     6684.74797174860}, 
    {     0.00000000071,  6.24412260280,     3894.18182954220}, 
    {     0.00000000079,  5.14539339999,     3532.06069281140}, 
    {     0.00000000080,  3.42045199039,     6525.80445396540}, 
    {     0.00000000061,  3.81929342821,     2942.46342329160}, 
    {     0.00000000066,  0.95264988100,    23384.28698689860}, 
    {     0.00000000062,  1.65751945223,     3583.34103067380}, 
    {     0.00000000062,  5.30607853843,     2544.31441988340}, 
    {     0.00000000042,  0.30552815689,     3339.63210563160}, 
    {     0.00000000037,  4.37754880706,     2787.04302385740}, 
    {     0.00000000043,  4.90457279180,     4292.33083295040}, 
    {     0.00000000036,  3.58183533863,     4690.47983635860}, 
    {     0.00000000034,  0.89018356943,    10025.36039844840}, 
    {     0.00000000032,  2.34732348899,     5088.62883976680}, 
    {     0.00000000028,  1.23206084526,     3723.50895892300}, 
    {     0.00000000026,  0.56214389305,      155.42039943420}, 
    {     0.00000000026,  4.11359839477,     6677.70173505060}, 
    {     0.00000000026,  0.37391494322,     2146.16541647520}, 
    {     0.00000000024,  5.78802013510,     5884.92684658320}, 
    {     0.00000000021,  2.91916849909,      529.69096509460}, 
    {     0.00000000019,  4.86965145048,     4136.91043351620}, 
    {     0.00000000023,  1.04314198221,     5486.77784317500}, 
    {     0.00000000018,  4.95637454569,     3149.16416058820}, 
    {     0.00000000017,  6.23546258970,     7079.37385680780}, 
    {     0.00000000017,  3.82096761296,     3341.59274776800}, 
    {     0.00000000019,  5.66874348929,     2388.89402044920}, 
    {     0.00000000015,  5.13426153783,     6489.77658728800}, 
    {     0.00000000014,  0.53723500958,     1990.74501704100}, 
    {     0.00000000014,  3.07166661567,     2957.71589447660}, 
    {     0.00000000012,  1.00141464760,     3340.62968035200}, 
    {     0.00000000012,  5.24418015401,     3340.59517304760}, 
    {     0.00000000013,  0.41162836180,     8962.45534991020}, 
    {     0.00000000012,  3.81140154428,     9866.41688066520}, 
    {     0.00000000012,  4.25382428399,     6151.53388830500}, 
    {     0.00000000015,  3.63297907536,     4535.05943692440}, 
    {     0.00000000012,  1.61461268629,     1592.59601363280}, 
    {     0.00000000010,  5.80958145013,     3333.49887969900}, 
    {     0.00000000010,  1.23772110632,     6836.64525283380}, 
    {     0.00000000009,  1.44366353557,    26724.89941359840}, 
    {     0.00000000008,  2.02732749775,     6923.95345737360}, 
    {     0.00000000009,  3.19116537565,     6438.49624942560}, 
    {     0.00000000008,  1.85197515729,     1194.44701022460}, 
    {     0.00000000008,  2.56762648035,      398.14900340820}, 
    {     0.00000000007,  3.69377532737,     4399.99435688900}, 
    {     0.00000000005,  4.73479766634,     6127.65545055720}, 
    {     0.00000000005,  0.39109547220,     5092.15195811580}, 
    {     0.00000000006,  1.41716854423,    13365.97282514820}, 
    {     0.00000000005,  3.98879770109,     6283.07584999140}, 
    {     0.00000000005,  1.86523815587,     1059.38193018920}, 
    {     0.00000000006,  5.52177150128,     7477.52286021600}, 
    {     0.00000000005,  1.92244747457,     2810.92146160520}, 
};


static const struct ln_vsop mars_latitude_b4[LAT_B4] = {
    {     0.00000006007,  3.37637101191,     3340.61242669980}, 
    {     0.00000006625,  0.00000000000,        0.00000000000}, 
    {     0.00000000464,  3.77202757150,    10021.83728009940}, 
    {     0.00000000405,  0.63107416776,     6681.22485339960}, 
    {     0.00000000299,  4.32966790803,    13362.44970679920}, 
    {     0.00000000109,  4.85358280107,    16703.06213349900}, 
    {     0.00000000077,  2.88080440451,     3496.03282613400}, 
    {     0.00000000039,  1.43197590360,     3185.19202726560}, 
    {     0.00000000031,  5.67989354532,     3337.08930835080}, 
    {     0.00000000031,  5.33373014736,    20043.67456019880}, 
    {     0.00000000017,  4.32019018052,     3097.88382272579}, 
    {     0.00000000013,  1.77444975035,     6525.80445396540}, 
    {     0.00000000010,  0.04059602724,     3583.34103067380}, 
    {     0.00000000007,  4.46709463778,     6684.74797174860}, 
    {     0.00000000006,  1.85656049405,     2787.04302385740}, 
    {     0.00000000006,  1.15875671922,     3894.18182954220}, 
    {     0.00000000006,  5.76437007548,    23384.28698689860}, 
    {     0.00000000003,  2.91488661915,     6836.64525283380}, 
};


static const struct ln_vsop mars_latitude_b5[LAT_B5] = {
    {     0.00000000368,  4.63460005338,     3340.61242669980}, 
    {     0.00000000045,  5.14206308865,     6681.22485339960}, 
    {     0.00000000035,  3.14159265359,        0.00000000000}, 
    {     0.00000000012,  2.68434578055,    13362.44970679920}, 
    {     0.00000000010,  4.43919916342,     3496.03282613400}, 
    {     0.00000000006,  1.70177189273,    10021.83728009940}, 
    {     0.00000000005,  3.20415104620,    16703.06213349900}, 
    {     0.00000000004,  6.15670065734,     3185.19202726560}, 
    {     0.00000000001,  3.71915090755,    20043.67456019880}, 
};


static const struct ln_vsop mars_radius_r0[RADIUS_R0] = {
    {     1.53033488271,  0.00000000000,        0.00000000000}, 
    {     0.14184953160,  3.47971283528,     3340.61242669980}, 
    {     0.00660776362,  3.81783443019,     6681.22485339960}, 
    {     0.00046179117,  4.15595316782,    10021.83728009940}, 
    {     0.00008109733,  5.55958416318,     2810.92146160520}, 
    {     0.00007485318,  1.77239078402,     5621.84292321040}, 
    {     0.00005523191,  1.36436303770,     2281.23049651060}, 
    {     0.00003825160,  4.49407183687,    13362.44970679920}, 
    {     0.00002306537,  0.09081579001,     2544.31441988340}, 
    {     0.00001999396,  5.36059617709,     3337.08930835080}, 
    {     0.00002484394,  4.92545639920,     2942.46342329160}, 
    {     0.00001960195,  4.74249437639,     3344.13554504880}, 
    {     0.00001167119,  2.11260868341,     5092.15195811580}, 
    {     0.00001102816,  5.00908403998,      398.14900340820}, 
    {     0.00000899066,  4.40791133207,      529.69096509460}, 
    {     0.00000992252,  5.83861961952,     6151.53388830500}, 
    {     0.00000807354,  2.10217065501,     1059.38193018920}, 
    {     0.00000797915,  3.44839203899,      796.29800681640}, 
    {     0.00000740975,  1.49906336885,     2146.16541647520}, 
    {     0.00000692339,  2.13378874689,     8962.45534991020}, 
    {     0.00000633144,  0.89353283242,     3340.59517304760}, 
    {     0.00000725583,  1.24516810723,     8432.76438481560}, 
    {     0.00000633140,  2.92430446399,     3340.62968035200}, 
    {     0.00000574355,  0.82896244455,     2914.01423582380}, 
    {     0.00000526166,  5.38292991236,     3738.76143010800}, 
    {     0.00000629978,  1.28737486495,     1751.53953141600}, 
    {     0.00000472775,  5.19850522346,     3127.31333126180}, 
    {     0.00000348095,  4.83219199976,    16703.06213349900}, 
    {     0.00000283713,  2.90692064724,     3532.06069281140}, 
    {     0.00000279543,  5.25749685380,     6283.07584999140}, 
    {     0.00000233857,  5.10545987572,     5486.77784317500}, 
    {     0.00000219427,  5.58340231744,      191.44826611160}, 
    {     0.00000269896,  3.76393625127,     5884.92684658320}, 
    {     0.00000208335,  5.25476078693,     3340.54511639700}, 
    {     0.00000275217,  2.90817482492,     1748.01641306700}, 
    {     0.00000275506,  1.21767950614,     6254.62666252360}, 
    {     0.00000239119,  2.03669934656,     1194.44701022460}, 
    {     0.00000223189,  4.19861535147,     3149.16416058820}, 
    {     0.00000182689,  5.08062725665,     6684.74797174860}, 
    {     0.00000186207,  5.69871572410,     6677.70173505060}, 
    {     0.00000176000,  5.95341919657,     3870.30339179440}, 
    {     0.00000178617,  4.18423004741,     3333.49887969900}, 
    {     0.00000208330,  4.84626439637,     3340.67973700260}, 
    {     0.00000228126,  3.25526555588,     6872.67311951120}, 
    {     0.00000144312,  0.21306219460,     5088.62883976680}, 
    {     0.00000163527,  3.79888811958,     4136.91043351620}, 
    {     0.00000133126,  1.53906679361,     7903.07341972100}, 
    {     0.00000141755,  2.47792380112,     4562.46099302120}, 
    {     0.00000114927,  4.31748869065,     1349.86740965880}, 
    {     0.00000118789,  2.12168482244,     1589.07289528380}, 
    {     0.00000102094,  6.18145185708,     9492.14631500480}, 
    {     0.00000128570,  5.49884728795,     8827.39026987480}, 
    {     0.00000111546,  0.55346108403,    11243.68584642080}, 
    {     0.00000082498,  1.62220096558,    11773.37681151540}, 
    {     0.00000083204,  0.61551135046,     8429.24126646660}, 
    {     0.00000084463,  0.62274409931,     1592.59601363280}, 
    {     0.00000086666,  1.74984525176,     2700.71514038580}, 
    {     0.00000071813,  2.47494065480,    12303.06777661000}, 
    {     0.00000085321,  1.61634750496,     4690.47983635860}, 
    {     0.00000063641,  2.67334163937,      426.59819087600}, 
    {     0.00000068601,  2.40188234283,     4399.99435688900}, 
    {     0.00000058559,  4.72052839990,      213.29909543800}, 
    {     0.00000062009,  1.10068565926,     1221.84856632140}, 
    {     0.00000066499,  2.21296335919,     6041.32756708560}, 
    {     0.00000055810,  1.23288066320,     3185.19202726560}, 
    {     0.00000054969,  5.72695354791,      951.71840625060}, 
    {     0.00000052430,  3.02368095530,     4292.33083295040}, 
    {     0.00000055688,  5.44688671707,     3723.50895892300}, 
    {     0.00000058959,  3.26242460622,     6681.24210705180}, 
    {     0.00000044638,  2.01459444131,     8031.09226305840}, 
    {     0.00000058959,  1.23165296790,     6681.20759974740}, 
    {     0.00000042439,  2.26554261514,      155.42039943420}, 
    {     0.00000038955,  2.57760417339,     3341.59274776800}, 
    {     0.00000051550,  5.72324451485,     7079.37385680780}, 
    {     0.00000048940,  5.61613493545,     3553.91152213780}, 
    {     0.00000045406,  5.43303278149,     6467.92575796160}, 
    {     0.00000036438,  4.43922435395,     3894.18182954220}, 
    {     0.00000035980,  1.15972378713,     2288.34404351140}, 
    {     0.00000035268,  5.49032233898,     1990.74501704100}, 
    {     0.00000042192,  1.63254827838,     5628.95647021120}, 
    {     0.00000044292,  5.00344221303,     5614.72937620960}, 
    {     0.00000033616,  5.17029030468,    20043.67456019880}, 
    {     0.00000043256,  1.03722397198,    11769.85369316640}, 
    {     0.00000039237,  1.24237030858,     3339.63210563160}, 
    {     0.00000031949,  4.59259676953,     2274.11694950980}, 
    {     0.00000030352,  2.44163963455,    11371.70468975820}, 
    {     0.00000032269,  2.38222363233,     4535.05943692440}, 
    {     0.00000031855,  4.37536980289,        3.52311834900}, 
    {     0.00000029342,  4.06035002188,     3097.88382272579}, 
    {     0.00000031967,  1.93969979134,      382.89653222320}, 
    {     0.00000026164,  5.58463559826,     9623.68827669120}, 
    {     0.00000027903,  4.25809486053,     3191.04922956520}, 
    {     0.00000033044,  0.85475620169,      553.56940284240}, 
    {     0.00000027544,  1.57668645170,     9595.23908922340}, 
    {     0.00000025163,  0.81337734264,    10713.99488132620}, 
    {     0.00000022045,  0.85711201558,     3319.83703120740}, 
    {     0.00000024759,  5.38993953923,     2818.03500860600}, 
    {     0.00000023352,  6.01458974590,     3496.03282613400}, 
    {     0.00000024723,  2.58025225634,     2803.80791460440}, 
    {     0.00000019361,  5.18528881954,     6681.29216370240}, 
    {     0.00000019118,  5.41969355400,    10025.36039844840}, 
    {     0.00000019361,  5.59378511334,     6681.15754309680}, 
    {     0.00000018331,  5.79565723310,     7064.12138562280}, 
    {     0.00000018188,  5.61299105522,        7.11354700080}, 
    {     0.00000020393,  4.53615443964,     6489.77658728800}, 
    {     0.00000021258,  6.19174428363,    14054.60730802600}, 
    {     0.00000017094,  1.54988538094,     2957.71589447660}, 
    {     0.00000022794,  3.41719468533,     7632.94325965020}, 
    {     0.00000020561,  2.98654120324,     3361.38782219220}, 
    {     0.00000017050,  6.15529583629,    10404.73381232260}, 
    {     0.00000018007,  2.81505100996,     4032.77002792660}, 
    {     0.00000016487,  3.84534133372,    10973.55568635000}, 
    {     0.00000016056,  0.92819026247,    14584.29827312060}, 
    {     0.00000021008,  2.38506850221,     4989.05918389720}, 
    {     0.00000016291,  1.92190075688,     7373.38245462640}, 
    {     0.00000016286,  6.28252184173,     7210.91581849420}, 
    {     0.00000018575,  4.07319565284,     2388.89402044920}, 
    {     0.00000015976,  4.58379703739,     3264.34635542420}, 
    {     0.00000019909,  2.73523951203,     5099.26550511660}, 
    {     0.00000019667,  1.86294734899,     3443.70520091840}, 
    {     0.00000016500,  4.14061657170,     7477.52286021600}, 
    {     0.00000019492,  6.03778625701,    10018.31416175040}, 
    {     0.00000015097,  2.65433832872,     2787.04302385740}, 
    {     0.00000019099,  0.22623513076,    13745.34623902240}, 
    {     0.00000017164,  3.18826299350,     3347.72597370060}, 
    {     0.00000013407,  2.12775612449,     3344.20285535160}, 
    {     0.00000015407,  2.20766468871,     2118.76386037840}, 
    {     0.00000017246,  3.67064642858,     3205.54734666440}, 
    {     0.00000013091,  4.27475419816,    14314.16811304980}, 
    {     0.00000016437,  2.86612474805,    14712.31711645800}, 
    {     0.00000016648,  4.52135149200,     6674.11130639880}, 
    {     0.00000013718,  1.68586111426,     3337.02199804800}, 
    {     0.00000011824,  0.19675650045,     3475.67750673520}, 
    {     0.00000011757,  3.23020638064,     5828.02847164760}, 
    {     0.00000011884,  4.82075035433,     7234.79425624200}, 
    {     0.00000010608,  1.73995972784,      639.89728631400}, 
    {     0.00000011143,  0.23833349966,    12832.75874170460}, 
    {     0.00000011028,  0.44555687290,    10213.28554621100}, 
    {     0.00000010238,  5.74731032428,      242.72860397400}, 
    {     0.00000010052,  2.45096419672,     4929.68532198360}, 
    {     0.00000010061,  0.78904152333,     9381.93999378540}, 
    {     0.00000010065,  5.37509927353,     5085.03841111500}, 
    {     0.00000011897,  0.79890074455,     3265.83082813250}, 
    {     0.00000008983,  0.96474320941,     4933.20844033260}, 
    {     0.00000008976,  4.18310051894,     9225.53927328300}, 
    {     0.00000008982,  1.98499607259,    15113.98923821520}, 
    {     0.00000008325,  1.93706224943,     1648.44675719740}, 
    {     0.00000007832,  2.04997038646,     1758.65307841680}, 
    {     0.00000007964,  3.92258783522,     2921.12778282460}, 
    {     0.00000010223,  2.66509814753,     2487.41604494780}, 
    {     0.00000008277,  0.94860765545,     2906.90068882300}, 
    {     0.00000007371,  0.84436508721,      692.15760122680}, 
    {     0.00000007529,  5.68043313811,    13916.01910964160}, 
    {     0.00000007907,  2.81314645975,    15643.68020330980}, 
    {     0.00000006956,  3.32212696002,     3230.40610548040}, 
    {     0.00000007426,  6.09654676653,     3583.34103067380}, 
    {     0.00000006402,  4.19806999276,     5202.35827933520}, 
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    {     0.00000000084,  5.31880055844,     4716.38622654560}, 
    {     0.00000000081,  5.46340742050,     3856.07629779280}, 
    {     0.00000000091,  2.82213463878,      367.22432896240}, 
    {     0.00000000076,  5.54629636453,     4349.16189758320}, 
    {     0.00000000073,  4.61913155968,     3288.35211178700}, 
    {     0.00000000097,  0.68615321372,    10006.58480891440}, 
    {     0.00000000071,  0.29424294238,     1324.94134054000}, 
    {     0.00000000074,  1.74142938655,    78263.70942472259}, 
    {     0.00000000076,  0.00928867044,     6534.41316687600}, 
    {     0.00000000084,  2.33518173212,     3738.74417645580}, 
    {     0.00000000075,  3.61437779765,    12306.59089495900}, 
    {     0.00000000085,  0.94196641948,     2146.18267012740}, 
    {     0.00000000071,  2.07200856102,     9124.92198604240}, 
    {     0.00000000071,  4.48060598672,     9153.90361602180}, 
    {     0.00000000073,  0.28701671181,    10654.62101941260}, 
    {     0.00000000072,  0.84342376295,     3334.54651107000}, 
    {     0.00000000094,  5.72469267962,      206.70073729660}, 
    {     0.00000000091,  5.12701600437,     3392.87274161260}, 
    {     0.00000000076,  5.96038992872,     3482.79105373600}, 
    {     0.00000000071,  1.16745785331,     1574.84580128220}, 
    {     0.00000000071,  1.08624489534,     3866.78027344540}, 
    {     0.00000000071,  3.83802267632,    25298.29315444680}, 
    {     0.00000000075,  4.30016984862,    10177.19036923080}, 
    {     0.00000000081,  5.71063897801,    14687.39104733920}, 
    {     0.00000000070,  0.07475004834,    12839.87228870540}, 
    {     0.00000000080,  5.87829926376,     3495.96551583120}, 
    {     0.00000000069,  0.30282686836,    12012.58229714040}, 
    {     0.00000000071,  2.07966257785,     1063.31408345230}, 
    {     0.00000000071,  0.12080952310,    27433.88921587499}, 
    {     0.00000000072,  1.77506111582,     3564.95722240170}, 
    {     0.00000000069,  0.33478558217,        5.52292430740}, 
    {     0.00000000068,  1.56404561711,     2398.55036473080}, 
    {     0.00000000090,  2.61953849393,     3346.67834232960}, 
    {     0.00000000068,  1.06108185791,      191.38095580880}, 
    {     0.00000000093,  3.72700623766,     2472.67876262220}, 
    {     0.00000000077,  0.87794040199,     2917.94638908690}, 
    {     0.00000000067,  3.29797798194,     8006.16619393960}, 
    {     0.00000000082,  4.33799969295,     9360.60435331840}, 
    {     0.00000000068,  4.84097033274,    12942.96506292400}, 
    {     0.00000000083,  5.35554906977,     2125.81009707640}, 
    {     0.00000000083,  1.82578570378,     3511.28529731900}, 
    {     0.00000000068,  2.68247854175,    20213.25474333179}, 
    {     0.00000000086,  0.81171860574,      209.77597708900}, 
    {     0.00000000084,  4.36595418339,     3738.77868376020}, 
    {     0.00000000071,  2.76447756531,    15650.79375031060}, 
    {     0.00000000066,  3.31414998734,     8830.91338822380}, 
    {     0.00000000090,  0.71593793107,     3451.79906898740}, 
    {     0.00000000067,  4.04202356962,     3930.20969621960}, 
    {     0.00000000068,  4.35822797929,    12299.54465826100}, 
    {     0.00000000073,  3.66802441649,      194.97138446060}, 
    {     0.00000000077,  5.89874180574,     4307.58330413540}, 
    {     0.00000000089,  2.09613892664,     5312.56460055460}, 
    {     0.00000000068,  1.05513114246,     1987.22189869200}, 
    {     0.00000000082,  5.86597589657,     7747.72033058960}, 
    {     0.00000000071,  0.65820952553,      860.30992875280}, 
    {     0.00000000064,  0.98960038205,     3376.17516116840}, 
    {     0.00000000067,  5.22683619088,    24606.13555322000}, 
    {     0.00000000070,  0.96227192685,     8428.83223155250}, 
    {     0.00000000064,  5.15148312244,     8966.38750317330}, 
    {     0.00000000062,  6.18276166360,     3966.28261901220}, 
    {     0.00000000061,  1.47350010728,     1685.05212250160}, 
    {     0.00000000069,  4.32901678608,     8436.69653807870}, 
    {     0.00000000064,  2.11869877898,     3305.04969223120}, 
    {     0.00000000079,  5.29501968122,     8322.55806359620}, 
    {     0.00000000060,  1.17940250396,    97670.38771289718}, 
    {     0.00000000060,  5.15547946009,     4665.55376723980}, 
    {     0.00000000061,  4.04008021030,     2942.48067694380}, 
    {     0.00000000061,  0.44282820959,     4686.95671800959}, 
    {     0.00000000079,  2.10625649179,     7917.30051372260}, 
    {     0.00000000075,  4.81216780547,    27299.24421193320}, 
    {     0.00000000058,  1.69747168940,    12082.65513417120}, 
    {     0.00000000075,  1.85618011420,    52566.19261584059}, 
    {     0.00000000057,  5.11652903646,     1898.33396428740}, 
    {     0.00000000075,  5.15830659680,    45884.96776244100}, 
    {     0.00000000060,  2.68566185208,     6283.05859633920}, 
    {     0.00000000056,  3.77198339507,      299.12639426920}, 
    {     0.00000000072,  0.05525158510,     6286.59896834040}, 
    {     0.00000000075,  5.79419108898,     1059.36467653700}, 
    {     0.00000000056,  0.47178586543,     1727.66109366820}, 
    {     0.00000000061,  2.00931045169,     2942.44616963940}, 
    {     0.00000000060,  2.60462801513,    30376.35263916660}, 
    {     0.00000000057,  4.18603648623,     4531.53631857540}, 
    {     0.00000000059,  1.95998946118,     7593.79509706520}, 
    {     0.00000000059,  0.11151543852,     5960.08562219340}, 
    {     0.00000000068,  3.50707258885,     7064.10413197060}, 
    {     0.00000000056,  2.43554289279,    11567.19126307820}, 
    {     0.00000000060,  0.23404709116,     2619.47319549360}, 
    {     0.00000000066,  2.94716590333,     8446.99147881720}, 
    {     0.00000000059,  5.49704665474,     7322.10246078180}, 
    {     0.00000000064,  3.95992112220,     3050.12694723020}, 
    {     0.00000000055,  2.19506741266,        7.04623669800}, 
    {     0.00000000058,  0.32431074295,    19645.52555679060}, 
    {     0.00000000075,  4.12415692769,    21150.81336588360}, 
    {     0.00000000075,  3.99896297048,     5483.25472482600}, 
    {     0.00000000057,  0.21772333641,    17402.33328172660}, 
    {     0.00000000069,  3.20209555520,    16066.06586147480}, 
    {     0.00000000056,  2.00267092675,    17660.30346405700}, 
    {     0.00000000060,  4.71643347424,     6283.09310364360}, 
    {     0.00000000054,  0.38782719267,      360.11078196160}, 
    {     0.00000000073,  3.41087754271,    14556.89671702380}, 
    {     0.00000000068,  5.74655335863,      987.74627292800}, 
};


static const struct ln_vsop mars_radius_r1[RADIUS_R1] = {
    {     0.01107433345,  2.03250524857,     3340.61242669980}, 
    {     0.00103175887,  2.37071847807,     6681.22485339960}, 
    {     0.00012877200,  0.00000000000,        0.00000000000}, 
    {     0.00010815880,  2.70888095665,    10021.83728009940}, 
    {     0.00001194550,  3.04702256206,    13362.44970679920}, 
    {     0.00000438582,  2.88835054603,     2281.23049651060}, 
    {     0.00000395700,  3.42323670971,     3344.13554504880}, 
    {     0.00000182576,  1.58427562964,     2544.31441988340}, 
    {     0.00000135851,  3.38507063082,    16703.06213349900}, 
    {     0.00000128199,  0.62991771813,     1059.38193018920}, 
    {     0.00000127059,  1.95391155885,      796.29800681640}, 
    {     0.00000118443,  2.99762091382,     2146.16541647520}, 
    {     0.00000128362,  6.04343227063,     3337.08930835080}, 
    {     0.00000087534,  3.42053385867,      398.14900340820}, 
    {     0.00000083021,  3.85575072018,     3738.76143010800}, 
    {     0.00000075604,  4.45097659377,     6151.53388830500}, 
    {     0.00000072002,  2.76443992447,      529.69096509460}, 
    {     0.00000066545,  2.54878381470,     1751.53953141600}, 
    {     0.00000054305,  0.67754203387,     8962.45534991020}, 
    {     0.00000051043,  3.72584855417,     6684.74797174860}, 
    {     0.00000066413,  4.40596377334,     1748.01641306700}, 
    {     0.00000047860,  2.28524521788,     2914.01423582380}, 
    {     0.00000049420,  5.72961379219,     3340.59517304760}, 
    {     0.00000049420,  1.47720011103,     3340.62968035200}, 
    {     0.00000057519,  0.54356133120,     1194.44701022460}, 
    {     0.00000048320,  2.58061402348,     3149.16416058820}, 
    {     0.00000036383,  6.02729341698,     3185.19202726560}, 
    {     0.00000037161,  5.81436290851,     1349.86740965880}, 
    {     0.00000036035,  5.89515829011,     3333.49887969900}, 
    {     0.00000031111,  0.97820401887,      191.44826611160}, 
    {     0.00000038957,  2.31902442004,     4136.91043351620}, 
    {     0.00000027256,  5.41369838171,     1592.59601363280}, 
    {     0.00000024302,  3.75838444077,      155.42039943420}, 
    {     0.00000022808,  1.74818178182,     5088.62883976680}, 
    {     0.00000022322,  0.93941901193,      951.71840625060}, 
    {     0.00000021712,  3.83569490817,     6283.07584999140}, 
    {     0.00000021302,  0.78030571909,     1589.07289528380}, 
    {     0.00000021631,  4.56903942095,     3532.06069281140}, 
    {     0.00000017957,  4.21923537063,     3870.30339179440}, 
    {     0.00000018241,  0.41334220202,     5486.77784317500}, 
    {     0.00000016250,  3.80772429678,     3340.54511639700}, 
    {     0.00000016803,  5.54855432911,     3097.88382272579}, 
    {     0.00000016852,  4.53696884484,     4292.33083295040}, 
    {     0.00000015749,  4.75766175289,     9492.14631500480}, 
    {     0.00000015747,  3.72356261757,    20043.67456019880}, 
    {     0.00000020429,  3.13541604634,     4690.47983635860}, 
    {     0.00000014699,  5.95340513928,     3894.18182954220}, 
    {     0.00000016251,  3.39910570757,     3340.67973700260}, 
    {     0.00000014256,  3.99914527335,     1990.74501704100}, 
    {     0.00000016529,  0.96740368703,     4399.99435688900}, 
    {     0.00000013011,  5.14215010082,     6677.70173505060}, 
    {     0.00000012482,  1.03238555854,     3341.59274776800}, 
    {     0.00000016454,  3.53827765951,     2700.71514038580}, 
    {     0.00000016167,  2.34891110870,      553.56940284240}, 
    {     0.00000013169,  0.41462220221,     5614.72937620960}, 
    {     0.00000011270,  1.02387117266,    12303.06777661000}, 
    {     0.00000012410,  6.23139144626,     5628.95647021120}, 
    {     0.00000012747,  0.69046237163,     3723.50895892300}, 
    {     0.00000011828,  6.25270937134,     2274.11694950980}, 
    {     0.00000010382,  1.23229650709,      426.59819087600}, 
    {     0.00000011207,  1.31732435116,     3496.03282613400}, 
    {     0.00000010345,  0.90062869301,     4535.05943692440}, 
    {     0.00000012214,  4.22347837212,     7079.37385680780}, 
    {     0.00000009764,  3.45310129694,      382.89653222320}, 
    {     0.00000008583,  1.16478890510,     2787.04302385740}, 
    {     0.00000007879,  5.73808303461,     2288.34404351140}, 
    {     0.00000009192,  1.81719352796,     6681.24210705180}, 
    {     0.00000007752,  4.15038634174,     6041.32756708560}, 
    {     0.00000009192,  6.06960723129,     6681.20759974740}, 
    {     0.00000009008,  2.58179552398,     2388.89402044920}, 
    {     0.00000006770,  0.24011880700,    11773.37681151540}, 
    {     0.00000007088,  3.51428380287,     8031.09226305840}, 
    {     0.00000009159,  3.90203365989,     3553.91152213780}, 
    {     0.00000007233,  3.70260535699,     2818.03500860600}, 
    {     0.00000006701,  4.25537421062,      242.72860397400}, 
    {     0.00000006534,  0.04317593308,     2957.71589447660}, 
    {     0.00000008783,  2.19764346848,     1221.84856632140}, 
    {     0.00000006540,  2.11811131682,     8429.24126646660}, 
    {     0.00000006835,  4.04527289029,    10025.36039844840}, 
    {     0.00000007279,  4.26969778292,     2803.80791460440}, 
    {     0.00000007679,  1.00816125095,     8432.76438481560}, 
    {     0.00000005736,  3.13988802339,      213.29909543800}, 
    {     0.00000005343,  3.78184164680,     5092.15195811580}, 
    {     0.00000005985,  2.96429619989,     6489.77658728800}, 
    {     0.00000005132,  3.98288020531,        7.11354700080}, 
    {     0.00000006264,  1.90345600186,     5621.84292321040}, 
    {     0.00000005238,  2.67050910776,     7477.52286021600}, 
    {     0.00000006264,  1.60046198142,     3347.72597370060}, 
    {     0.00000006527,  2.76220386403,     3339.63210563160}, 
    {     0.00000004594,  1.82031785094,     2810.92146160520}, 
    {     0.00000005460,  4.60869963415,     3583.34103067380}, 
    {     0.00000004730,  0.90611934427,     5099.26550511660}, 
    {     0.00000005484,  4.91405753832,     7632.94325965020}, 
    {     0.00000004002,  4.14100005210,     9623.68827669120}, 
    {     0.00000003836,  0.03411499404,     7234.79425624200}, 
    {     0.00000003618,  5.76553319747,     4933.20844033260}, 
    {     0.00000003747,  0.08776717073,     6525.80445396540}, 
    {     0.00000003016,  3.73804058695,     6681.29216370240}, 
    {     0.00000003975,  4.91286826343,     2942.46342329160}, 
    {     0.00000003911,  0.67457174687,     3127.31333126180}, 
    {     0.00000003923,  3.07698893109,        3.52311834900}, 
    {     0.00000003943,  0.53936955267,     5884.92684658320}, 
    {     0.00000002902,  4.66228680082,     7210.91581849420}, 
    {     0.00000002803,  1.00505054832,     7064.12138562280}, 
    {     0.00000003152,  4.54611126545,     2487.41604494780}, 
    {     0.00000002797,  0.05226680768,      639.89728631400}, 
    {     0.00000002758,  5.17057629399,     5828.02847164760}, 
    {     0.00000003020,  4.14658810846,     6681.15754309680}, 
    {     0.00000003000,  0.82762095066,     5085.03841111500}, 
    {     0.00000003022,  2.59437829291,     2906.90068882300}, 
    {     0.00000002673,  0.69433657973,     2699.73481931760}, 
    {     0.00000002593,  1.08691889359,     4929.68532198360}, 
    {     0.00000003127,  0.99947199034,     2118.76386037840}, 
    {     0.00000002597,  5.01157388627,    10018.31416175040}, 
    {     0.00000002606,  5.34395258978,    10973.55568635000}, 
    {     0.00000002779,  3.98360727591,     6467.92575796160}, 
    {     0.00000002457,  1.52659064342,     6836.64525283380}, 
    {     0.00000002381,  3.93615187831,    11371.70468975820}, 
    {     0.00000002584,  5.08907827632,    12832.75874170460}, 
    {     0.00000002204,  0.18721790349,     9595.23908922340}, 
    {     0.00000002127,  5.69525267283,     3191.04922956520}, 
    {     0.00000002065,  3.54230184958,     1066.49547719000}, 
    {     0.00000001862,  5.01664572032,     3475.67750673520}, 
    {     0.00000002077,  1.30210079493,     7740.60678358880}, 
    {     0.00000001834,  5.68364410455,     3319.83703120740}, 
    {     0.00000002026,  6.16037765302,     1744.42598441520}, 
    {     0.00000001705,  2.21753874961,     2921.12778282460}, 
    {     0.00000001836,  6.16475140098,     8425.65083781480}, 
    {     0.00000002060,  6.24256627641,     6674.11130639880}, 
    {     0.00000001735,  4.58252413180,    10419.98628350760}, 
    {     0.00000001853,  1.36791191191,    15643.68020330980}, 
    {     0.00000001683,  1.92963115929,     3767.21061757580}, 
    {     0.00000001955,  0.46151752408,    10575.40668294180}, 
    {     0.00000001800,  2.30912443204,     3355.86489788480}, 
    {     0.00000001761,  5.87259776407,     3320.25710730100}, 
    {     0.00000001440,  2.15100457092,    10021.85453375160}, 
    {     0.00000001845,  4.06143234617,    23384.28698689860}, 
    {     0.00000001419,  4.64964683208,     4562.46099302120}, 
    {     0.00000001410,  1.50439659549,     3325.35995551480}, 
    {     0.00000001435,  0.12022404881,    10021.82002644720}, 
    {     0.00000001446,  0.55888114207,    15113.98923821520}, 
    {     0.00000001334,  1.25480751834,     7875.67186362420}, 
    {     0.00000001442,  1.38958372017,     6682.20517446780}, 
    {     0.00000001601,  4.34240972038,     5331.35744374080}, 
    {     0.00000001377,  0.14567625356,     1758.65307841680}, 
    {     0.00000001283,  5.78388498920,    14584.29827312060}, 
    {     0.00000001281,  1.35158715330,    10404.73381232260}, 
    {     0.00000001255,  6.02547192213,     3264.34635542420}, 
    {     0.00000001471,  0.34647878204,     8969.56889691100}, 
    {     0.00000001237,  1.88316546445,    10177.25767953360}, 
    {     0.00000001554,  5.93165013851,     8439.87793181640}, 
    {     0.00000001185,  4.18096920842,     3360.96774609859}, 
    {     0.00000001192,  0.89923984424,    13916.01910964160}, 
    {     0.00000001331,  1.86674667785,      692.15760122680}, 
    {     0.00000001190,  4.29364281529,     6894.52394883760}, 
    {     0.00000001303,  1.44666271090,     6254.62666252360}, 
    {     0.00000001141,  0.15138021311,     3134.42687826260}, 
    {     0.00000001498,  1.54298726882,     3361.38782219220}, 
    {     0.00000001061,  0.67393132017,     3344.20285535160}, 
    {     0.00000001210,  0.85308958022,     3120.19978426100}, 
    {     0.00000001003,  1.28017736997,     4569.57454002200}, 
    {     0.00000001056,  0.13188094879,      522.57741809380}, 
    {     0.00000001011,  5.77318421567,    14314.16811304980}, 
    {     0.00000001172,  2.99768268266,     6247.51311552280}, 
    {     0.00000001071,  0.24747292047,     3337.02199804800}, 
    {     0.00000001088,  2.57510503125,     6261.74020952440}, 
    {     0.00000001033,  5.69839016800,      536.80451209540}, 
    {     0.00000000870,  1.50282095865,     6127.65545055720}, 
    {     0.00000000952,  2.92551885687,     5729.50644714900}, 
    {     0.00000001113,  2.84407720846,      640.87760738220}, 
    {     0.00000000861,  3.21490378166,     3914.95722503460}, 
    {     0.00000000873,  5.26929669197,    10213.28554621100}, 
    {     0.00000001068,  0.49291392496,    11243.68584642080}, 
    {     0.00000000802,  3.33123564567,     9830.38901398780}, 
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    {     0.00000000086,  4.69272071417,    14061.72085502680}, 
    {     0.00000000077,  5.64501410813,     3209.07046501340}, 
    {     0.00000000080,  5.70275817485,    10156.90236013480}, 
    {     0.00000000075,  3.83222347813,    39048.32250960720}, 
    {     0.00000000071,  0.76956199701,     7366.26890762560}, 
    {     0.00000000084,  0.79243785412,    16276.46394262300}, 
    {     0.00000000098,  2.04888453127,    15265.88651930040}, 
    {     0.00000000084,  4.65013165954,     6947.83189512140}, 
    {     0.00000000073,  4.30089715672,    21548.96236929180}, 
    {     0.00000000086,  1.50050122351,     5989.06725217280}, 
    {     0.00000000070,  2.69225539304,     3296.89351439480}, 
    {     0.00000000094,  0.74409756620,     5244.04923920100}, 
    {     0.00000000074,  2.27409026869,     4845.90023579280}, 
    {     0.00000000071,  3.75623870844,    28628.33622609960}, 
    {     0.00000000067,  3.31991953846,     6414.61781167780}, 
    {     0.00000000067,  1.32197410604,    23546.75362303080}, 
    {     0.00000000065,  2.68548224676,     4186.69526145100}, 
    {     0.00000000064,  3.98415414793,     3368.01398279660}, 
    {     0.00000000065,  4.15810281695,     3340.19235060619}, 
    {     0.00000000073,  2.84956464399,     8542.97070603500}, 
    {     0.00000000064,  1.07959823787,     6944.30877677240}, 
    {     0.00000000064,  1.20206773863,       38.13303563780}, 
    {     0.00000000079,  1.01784404862,     7321.12213971360}, 
    {     0.00000000070,  3.81533325092,     6578.13207918100}, 
    {     0.00000000063,  0.67886798875,     6688.27109009760}, 
    {     0.00000000086,  2.24834434956,     3232.94890276120}, 
    {     0.00000000074,  3.63312603513,    15906.76412668260}, 
    {     0.00000000061,  5.69343218974,     4459.36821880260}, 
    {     0.00000000068,  5.10830400193,     9485.03276800400}, 
    {     0.00000000061,  1.95896237186,    12199.97500239140}, 
    {     0.00000000076,  0.43724958811,     5032.77809620220}, 
    {     0.00000000062,  3.22645996942,     2540.79130153440}, 
    {     0.00000000061,  4.22937427795,     1854.63230563460}, 
    {     0.00000000070,  1.02515278218,     6621.85099148600}, 
    {     0.00000000060,  1.09184289831,    10124.93005431800}, 
    {     0.00000000060,  4.72802697102,    16865.52876963120}, 
    {     0.00000000059,  2.92995535821,     9886.77220006400}, 
    {     0.00000000058,  4.87086894257,    48300.16010269000}, 
    {     0.00000000058,  0.43992500862,     6418.14093002680}, 
    {     0.00000000058,  5.73619727103,     2008.55753915900}, 
    {     0.00000000072,  4.52406363260,    16304.91313009080}, 
    {     0.00000000067,  0.75347219892,    16703.04487984680}, 
    {     0.00000000070,  4.09500525151,     3416.87849797540}, 
    {     0.00000000080,  1.80777950075,      931.36308685180}, 
    {     0.00000000060,  4.92798256747,     3391.89276456221}, 
    {     0.00000000058,  2.45928697672,     4005.36847182980}, 
    {     0.00000000075,  4.81816499658,     3289.33208883739}, 
    {     0.00000000058,  1.73479637157,     2409.24933984800}, 
    {     0.00000000062,  5.24555453429,    17101.21113690720}, 
    {     0.00000000055,  3.59862329711,     7322.10246078180}, 
    {     0.00000000060,  0.91598691483,    10018.24685144760}, 
    {     0.00000000054,  5.54310937490,     2604.73591316800}, 
    {     0.00000000057,  0.39808125859,    18451.07854656599}, 
    {     0.00000000059,  2.02922256380,    45486.81875903279}, 
    {     0.00000000068,  2.78497806929,    16703.07938715119}, 
    {     0.00000000054,  1.76917054114,     3510.19260983280}, 
    {     0.00000000063,  2.80264902488,    16894.51039961060}, 
    {     0.00000000074,  1.36214292325,    10025.42770875120}, 
    {     0.00000000063,  2.41547192168,       59.37386191360}, 
    {     0.00000000054,  1.06826755543,     8948.22825590860}, 
    {     0.00000000051,  1.64684042106,     3472.15438838620}, 
    {     0.00000000052,  3.43538989813,    14867.73751589219}, 
    {     0.00000000062,  0.86680408610,    17468.85519794540}, 
    {     0.00000000051,  2.12159286185,     2412.77245819700}, 
    {     0.00000000056,  6.11996315499,    17085.95866572220}, 
    {     0.00000000053,  2.94662143572,    11527.12508919240}, 
    {     0.00000000050,  3.17196717347,     2111.65031337760}, 
    {     0.00000000055,  5.72607545560,    10706.88133432540}, 
    {     0.00000000062,  0.57333106196,     3171.03224356680}, 
    {     0.00000000053,  1.29021847041,     6652.77566593180}, 
    {     0.00000000052,  4.17299292219,     6106.88005506480}, 
    {     0.00000000065,  3.82721710324,    18208.34994259200}, 
    {     0.00000000065,  5.11165617529,     3113.13629391080}, 
    {     0.00000000048,  3.04479041123,     4140.43355186520}, 
    {     0.00000000048,  5.15462485717,    12012.58229714040}, 
    {     0.00000000049,  2.53202412418,    10448.43547097540}, 
    {     0.00000000055,  0.78890011077,    11769.85369316640}, 
    {     0.00000000047,  3.65081479882,     9872.27408296480}, 
    {     0.00000000047,  2.74355062408,    14577.18472611980}, 
    {     0.00000000051,  4.86147404192,     1485.98012106520}, 
    {     0.00000000059,  2.96261275062,    14071.43950907579}, 
    {     0.00000000060,  1.59668057901,     4025.65648092580}, 
    {     0.00000000045,  1.38985168616,     1272.68102562720}, 
    {     0.00000000046,  4.84193245992,    32124.36905223359}, 
    {     0.00000000048,  4.20779723621,    43340.65334255760}, 
    {     0.00000000047,  1.43502382920,     2938.94030494260}, 
    {     0.00000000058,  4.41305155897,     1478.86657406440}, 
    {     0.00000000045,  5.07966377852,     3318.76159737340}, 
    {     0.00000000058,  5.58121433180,     6643.09181776180}, 
    {     0.00000000047,  1.08172284939,     3448.27595063840}, 
    {     0.00000000048,  5.02446939402,     6645.19698672220}, 
    {     0.00000000044,  4.02177323039,     9389.05354078620}, 
    {     0.00000000042,  0.75715065967,     6357.71943674220}, 
    {     0.00000000042,  0.28202781151,    10001.48196070061}, 
    {     0.00000000042,  5.05676915852,     3397.51080163540}, 
    {     0.00000000043,  4.94357970653,    18052.92954315780}, 
    {     0.00000000050,  4.04580413243,     5835.14201864840}, 
    {     0.00000000046,  0.42891568037,    14128.24277124560}, 
    {     0.00000000043,  4.15051754642,     8535.85715903420}, 
    {     0.00000000053,  6.08293348275,     3377.21779200400}, 
    {     0.00000000041,  1.24482327948,     3212.59358336240}, 
    {     0.00000000041,  5.60183242162,      685.04405422600}, 
    {     0.00000000055,  2.49939849707,     8186.51266249260}, 
    {     0.00000000041,  5.04767355904,     6571.01853218020}, 
    {     0.00000000042,  3.00593850304,    10037.08975128440}, 
    {     0.00000000042,  2.08907550710,    13363.43002786740}, 
    {     0.00000000041,  0.56957277734,    20995.39296644940}, 
    {     0.00000000045,  1.33351374757,      632.78373931320}, 
    {     0.00000000046,  0.81640935106,    45884.96776244100}, 
    {     0.00000000040,  5.83979846235,      846.08283475120}, 
    {     0.00000000041,  0.05913112284,    21150.81336588360}, 
    {     0.00000000044,  2.89985709529,     6872.67311951120}, 
    {     0.00000000046,  4.79599204822,     1835.32461760680}, 
    {     0.00000000045,  1.98433687681,     1861.74585263540}, 
    {     0.00000000040,  4.76232751326,     4392.88080988820}, 
    {     0.00000000044,  4.30367510983,    21000.91589075680}, 
    {     0.00000000040,  6.09284885194,     7483.58877584580}, 
    {     0.00000000040,  2.33956668789,    12729.66596748600}, 
    {     0.00000000046,  2.86512929328,    38650.17350619900}, 
    {     0.00000000038,  3.65846461938,    29698.28751133580}, 
    {     0.00000000038,  2.26400097984,    38407.44490222499}, 
    {     0.00000000038,  4.62487442464,    13532.02988993220}, 
    {     0.00000000045,  0.05726736439,     8226.57883637840}, 
    {     0.00000000043,  5.28854105201,     3274.12501778540}, 
    {     0.00000000037,  4.75280838392,    30065.51184029820}, 
    {     0.00000000047,  6.25707790441,    24606.13555322000}, 
    {     0.00000000037,  5.02115296017,    11128.97608578420}, 
    {     0.00000000039,  1.71554278762,     7696.88787128380}, 
    {     0.00000000037,  4.34652985120,     3283.71405176420}, 
    {     0.00000000037,  3.91795548862,     9945.57120882380}, 
    {     0.00000000038,  1.54872687701,     6740.59871531320}, 
    {     0.00000000036,  6.11671952560,     9947.05568153210}, 
    {     0.00000000036,  4.61440005357,     6901.63749583840}, 
    {     0.00000000038,  0.44080908793,    24491.42579258340}, 
    {     0.00000000036,  1.73681874925,     3468.63127003720}, 
    {     0.00000000041,  5.69294900570,    26087.90314157420}, 
    {     0.00000000046,  4.24370266362,     3074.00538497800}, 
    {     0.00000000038,  0.72727556007,    26084.02180621620}, 
    {     0.00000000035,  0.09307361585,     8742.04270747140}, 
    {     0.00000000035,  1.35173564664,     7218.02936549500}, 
    {     0.00000000038,  5.04852696556,    16066.06586147480}, 
    {     0.00000000039,  4.09330106885,    28783.75662553379}, 
    {     0.00000000035,  2.18607267347,     8859.36257569160}, 
    {     0.00000000034,  3.37294996504,    48429.28218232440}, 
    {     0.00000000037,  3.20773047278,    41748.05732892480}, 
    {     0.00000000036,  1.14449536410,    15650.79375031060}, 
    {     0.00000000043,  2.47145616667,    10020.85695903120}, 
    {     0.00000000040,  6.03176945066,    17810.20093918380}, 
    {     0.00000000034,  0.51621135764,     1107.13880568480}, 
    {     0.00000000038,  5.52686444444,     3742.28454845700}, 
    {     0.00000000035,  4.07971812965,     8646.06348025360}, 
    {     0.00000000037,  0.76802632064,    35464.98147893340}, 
    {     0.00000000034,  0.48466144733,    38805.59390563319}, 
    {     0.00000000044,  4.85886492681,     6604.95878212400}, 
    {     0.00000000033,  0.15905665569,    10787.63034454580}, 
    {     0.00000000033,  6.26077209051,     4106.40549114620}, 
    {     0.00000000032,  4.72374245003,     8827.39026987480}, 
    {     0.00000000034,  1.67384584037,    40398.18991926600}, 
    {     0.00000000038,  3.42695313525,    37703.97802425580}, 
    {     0.00000000037,  5.01873798104,    13575.74880223720}, 
    {     0.00000000043,  4.79904796675,     5195.24473233440}, 
    {     0.00000000038,  2.54832320063,    10184.30391623160}, 
    {     0.00000000032,  0.26465341730,     3029.77162783140}, 
    {     0.00000000032,  6.21574097484,    15110.46611986620}, 
    {     0.00000000031,  3.63433062848,    45088.66975562460}, 
    {     0.00000000042,  0.55440675602,    32920.66705904999}, 
    {     0.00000000035,  3.96268115235,     3185.25933756840}, 
    {     0.00000000033,  5.88039450059,    19403.77727388480}, 
    {     0.00000000041,  4.27695289187,     7747.72033058960}, 
    {     0.00000000033,  5.41476981924,    20735.83216142559}, 
    {     0.00000000041,  4.13964021510,    12516.36687204800}, 
    {     0.00000000036,  6.22368196486,     4356.27544458400}, 
    {     0.00000000031,  1.81900571208,    24093.27678917520}, 
    {     0.00000000041,  2.61892942249,    24076.44458812540}, 
    {     0.00000000030,  1.25750331570,    34363.36559755600}, 
    {     0.00000000035,  4.30790850908,     4447.75123238460}, 
    {     0.00000000034,  2.15402582261,    12502.13977804640}, 
    {     0.00000000030,  1.74402934752,    10177.19036923080}, 
    {     0.00000000034,  4.98491983613,    20199.02764933019}, 
    {     0.00000000029,  0.38968519354,    35707.71008290740}, 
    {     0.00000000035,  1.98847450868,    14556.89671702380}, 
    {     0.00000000032,  0.36447448811,     5466.42252377620}, 
    {     0.00000000029,  2.84335822989,     3651.45322556820}, 
    {     0.00000000029,  1.70561861073,    42146.20633233299}, 
    {     0.00000000029,  6.27427740112,    31022.75317085620}, 
    {     0.00000000029,  4.85775467825,       36.02786667740}, 
    {     0.00000000029,  0.65663514164,     3344.11829139661}, 
    {     0.00000000039,  2.60584004585,     6679.74038069130}, 
    {     0.00000000031,  4.96068967529,    15423.26756087100}, 
    {     0.00000000032,  4.30747041560,    30376.35263916660}, 
    {     0.00000000031,  4.97488131714,    48031.13317891620}, 
    {     0.00000000036,  5.21102353378,      860.30992875280}, 
    {     0.00000000029,  2.68740712720,     3344.15279870100}, 
    {     0.00000000029,  4.89226176414,    14469.58851248400}, 
    {     0.00000000035,  0.63682098833,    23553.86717003160}, 
    {     0.00000000028,  3.93317215375,     2655.56837247380}, 
    {     0.00000000028,  4.95417710116,      792.77488846740}, 
    {     0.00000000031,  1.20412048035,    16328.72425753579}, 
    {     0.00000000033,  2.23175098152,    44768.09940987860}, 
    {     0.00000000033,  5.53387746412,    38086.87455647900}, 
    {     0.00000000028,  5.39448318150,     1250.83019630080}, 
    {     0.00000000034,  0.46215642912,     2751.54759969160}, 
    {     0.00000000031,  6.25053987025,    17388.10618772499}, 
    {     0.00000000028,  1.84806130514,     2075.04494807340}, 
    {     0.00000000029,  4.75344799610,    28230.18722269139}, 
    {     0.00000000028,  4.36162258057,    39203.74290904139}, 
    {     0.00000000032,  5.19762814944,     1214.80232962340}, 
    {     0.00000000027,  1.83675735374,    45494.58142974879}, 
    {     0.00000000028,  4.99070749177,     6593.91664885980}, 
    {     0.00000000027,  3.31433250805,    12942.96506292400}, 
    {     0.00000000029,  4.94569969969,       87.30820453981}, 
    {     0.00000000027,  1.32843166459,     7203.80227149340}, 
};


static const struct ln_vsop mars_radius_r2[RADIUS_R2] = {
    {     0.00044242249,  0.47930604954,     3340.61242669980}, 
    {     0.00008138042,  0.86998389204,     6681.22485339960}, 
    {     0.00001274915,  1.22593985222,    10021.83728009940}, 
    {     0.00000187388,  1.57298976045,    13362.44970679920}, 
    {     0.00000040745,  1.97082077028,     3344.13554504880}, 
    {     0.00000052395,  3.14159265359,        0.00000000000}, 
    {     0.00000026617,  1.91665337822,    16703.06213349900}, 
    {     0.00000017828,  4.43491476419,     2281.23049651060}, 
    {     0.00000011713,  4.52509926559,     3185.19202726560}, 
    {     0.00000010210,  5.39147322060,     1059.38193018920}, 
    {     0.00000009950,  0.41865678448,      796.29800681640}, 
    {     0.00000009236,  4.53559625376,     2146.16541647520}, 
    {     0.00000007299,  3.14214513120,     2544.31441988340}, 
    {     0.00000007214,  2.29302335628,     6684.74797174860}, 
    {     0.00000006810,  5.26707245601,      155.42039943420}, 
    {     0.00000006526,  2.30772456100,     3738.76143010800}, 
    {     0.00000007783,  5.93373461009,     1748.01641306700}, 
    {     0.00000005840,  1.05191820290,     1349.86740965880}, 
    {     0.00000006750,  5.30191763402,     1194.44701022460}, 
    {     0.00000004695,  0.76881032874,     3097.88382272579}, 
    {     0.00000005390,  1.00200068360,     3149.16416058820}, 
    {     0.00000004406,  2.45557331437,      951.71840625060}, 
    {     0.00000004286,  3.89642578846,     1592.59601363280}, 
    {     0.00000003516,  1.84991934524,      398.14900340820}, 
    {     0.00000003699,  2.26016989021,    20043.67456019880}, 
    {     0.00000003378,  3.81703201748,     1751.53953141600}, 
    {     0.00000004585,  0.80785643853,     4136.91043351620}, 
    {     0.00000003201,  2.11661594157,     5614.72937620960}, 
    {     0.00000003620,  1.32428600053,     3333.49887969900}, 
    {     0.00000002915,  1.19342490174,      529.69096509460}, 
    {     0.00000002979,  2.86468474914,     6151.53388830500}, 
    {     0.00000003057,  4.55288594507,     5628.95647021120}, 
    {     0.00000002906,  1.20300479533,     3894.18182954220}, 
    {     0.00000003848,  3.86071515455,      553.56940284240}, 
    {     0.00000002819,  2.48714583532,     1990.74501704100}, 
    {     0.00000002657,  6.07409846258,     4292.33083295040}, 
    {     0.00000002698,  2.92100135189,     3496.03282613400}, 
    {     0.00000002396,  5.94193484091,     2787.04302385740}, 
    {     0.00000002263,  2.56188049651,      191.44826611160}, 
    {     0.00000002169,  5.36834559071,     8962.45534991020}, 
    {     0.00000002149,  2.74919289456,      242.72860397400}, 
    {     0.00000002218,  1.85260509629,     3337.08930835080}, 
    {     0.00000001998,  5.76396921426,     3341.59274776800}, 
    {     0.00000001999,  3.82347205028,     2914.01423582380}, 
    {     0.00000001835,  5.68648448195,     1589.07289528380}, 
    {     0.00000001810,  3.32122811143,     5088.62883976680}, 
    {     0.00000001968,  4.17404480033,     3340.59517304760}, 
    {     0.00000002411,  4.68376177281,     4690.47983635860}, 
    {     0.00000001967,  6.20570363430,     3340.62968035200}, 
    {     0.00000001626,  5.67648778513,     4535.05943692440}, 
    {     0.00000002161,  1.07446445419,     2388.89402044920}, 
    {     0.00000001965,  3.10811453974,     3583.34103067380}, 
    {     0.00000001985,  5.75867975763,     4399.99435688900}, 
    {     0.00000001504,  4.95929390466,      382.89653222320}, 
    {     0.00000001276,  4.82147500391,     2957.71589447660}, 
    {     0.00000001475,  2.22614544794,     3723.50895892300}, 
    {     0.00000001196,  3.26743061042,     9492.14631500480}, 
    {     0.00000001349,  4.87558985925,     6525.80445396540}, 
    {     0.00000001436,  2.69754023270,     7079.37385680780}, 
    {     0.00000001223,  2.61880227353,    10025.36039844840}, 
    {     0.00000001402,  5.19177439326,     2700.71514038580}, 
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    {     0.00000000020,  0.86927302126,     3399.98628861340}, 
    {     0.00000000018,  4.37088769243,     3651.45322556820}, 
    {     0.00000000022,  4.79007467235,    11614.43329373220}, 
    {     0.00000000019,  5.80539564686,    21795.21409161479}, 
    {     0.00000000017,  2.62698055094,     6872.67311951120}, 
    {     0.00000000020,  4.13854946023,    16699.53901514999}, 
    {     0.00000000018,  2.69537794731,    27682.14074415640}, 
    {     0.00000000017,  2.35800085725,     7788.36365908440}, 
    {     0.00000000016,  5.12979256980,     1744.42598441520}, 
    {     0.00000000019,  4.36117042303,    11780.49035851620}, 
    {     0.00000000017,  3.98180845854,    18606.49894600020}, 
    {     0.00000000020,  5.29535152048,    13936.79450513400}, 
    {     0.00000000018,  0.90866227881,    27433.88921587499}, 
    {     0.00000000018,  1.15898054343,      220.41264243880}, 
    {     0.00000000021,  1.07415905494,    11769.85369316640}, 
    {     0.00000000018,  3.61054156740,     9485.03276800400}, 
    {     0.00000000020,  5.54806425258,    14128.24277124560}, 
    {     0.00000000015,  4.19346479448,    23937.85638974100}, 
    {     0.00000000019,  2.49025671313,    24341.52831745660}, 
    {     0.00000000015,  6.22588872744,     8799.98871377800}, 
    {     0.00000000014,  2.27829337274,     4447.75123238460}, 
    {     0.00000000015,  1.86263855445,     2921.12778282460}, 
    {     0.00000000014,  3.59449757262,     3074.00538497800}, 
    {     0.00000000016,  4.04109191506,     3134.42687826260}, 
    {     0.00000000018,  1.50064662425,    19406.67828817460}, 
    {     0.00000000014,  4.63902518517,    11527.12508919240}, 
    {     0.00000000019,  5.20657856071,    32920.66705904999}, 
    {     0.00000000018,  5.05191310629,     3603.69635007260}, 
};


static const struct ln_vsop mars_radius_r3[RADIUS_R3] = {
    {     0.00001113108,  5.14987305093,     3340.61242669980}, 
    {     0.00000424447,  5.61343952053,     6681.22485339960}, 
    {     0.00000100044,  5.99727457548,    10021.83728009940}, 
    {     0.00000019606,  0.07631453783,    13362.44970679920}, 
    {     0.00000003478,  0.42912010211,    16703.06213349900}, 
    {     0.00000004693,  3.14159265359,        0.00000000000}, 
    {     0.00000002870,  0.44692002393,     3344.13554504880}, 
    {     0.00000002428,  3.02114808809,     3185.19202726560}, 
    {     0.00000000687,  0.80560442666,     6684.74797174860}, 
    {     0.00000000578,  0.77849309402,    20043.67456019880}, 
    {     0.00000000540,  3.86818792995,     1059.38193018920}, 
    {     0.00000000468,  4.52509679627,     3496.03282613400}, 
    {     0.00000000487,  1.60861075208,     3583.34103067380}, 
    {     0.00000000362,  4.42325508671,     2787.04302385740}, 
    {     0.00000000397,  5.72008479880,     3149.16416058820}, 
    {     0.00000000299,  0.75708428385,     3738.76143010800}, 
    {     0.00000000352,  5.55622002342,     4136.91043351620}, 
    {     0.00000000316,  3.37609906858,     6525.80445396540}, 
    {     0.00000000234,  2.13923292630,     3097.88382272579}, 
    {     0.00000000214,  4.20457486315,     3341.59274776800}, 
    {     0.00000000214,  0.56472270648,      155.42039943420}, 
    {     0.00000000201,  2.35183535764,     1592.59601363280}, 
    {     0.00000000206,  0.96951658721,     1990.74501704100}, 
    {     0.00000000231,  5.82604761072,     2388.89402044920}, 
    {     0.00000000163,  4.15852184076,     4535.05943692440}, 
    {     0.00000000148,  3.28924896754,     2957.71589447660}, 
    {     0.00000000155,  5.12396546072,      796.29800681640}, 
    {     0.00000000154,  1.13809634337,    10025.36039844840}, 
    {     0.00000000158,  3.76267616455,     1194.44701022460}, 
    {     0.00000000134,  5.57743966517,     3894.18182954220}, 
    {     0.00000000145,  3.02382693331,     3337.08930835080}, 
    {     0.00000000147,  4.25259909424,     4399.99435688900}, 
    {     0.00000000100,  4.26399779787,     1589.07289528380}, 
    {     0.00000000091,  6.12313839857,     6489.77658728800}, 
    {     0.00000000100,  1.12570940535,    23384.28698689860}, 
    {     0.00000000100,  1.17079212321,     7079.37385680780}, 
    {     0.00000000076,  6.00434755125,      529.69096509460}, 
    {     0.00000000076,  5.93213294948,     7477.52286021600}, 
    {     0.00000000069,  1.70323063297,     9492.14631500480}, 
    {     0.00000000069,  3.69074496365,     8962.45534991020}, 
    {     0.00000000068,  0.15861692654,     3870.30339179440}, 
    {     0.00000000061,  4.14189658327,     4292.33083295040}, 
    {     0.00000000063,  1.94108069224,     6923.95345737360}, 
    {     0.00000000060,  4.28936601254,    12303.06777661000}, 
    {     0.00000000065,  1.11375145336,     6151.53388830500}, 
    {     0.00000000075,  4.71644556135,     3347.72597370060}, 
    {     0.00000000056,  2.74147961496,     4933.20844033260}, 
    {     0.00000000053,  4.77467577413,     6127.65545055720}, 
    {     0.00000000050,  2.57807944338,     3340.59517304760}, 
    {     0.00000000049,  3.72534850744,     9866.41688066520}, 
    {     0.00000000050,  4.60885064189,     3340.62968035200}, 
    {     0.00000000042,  6.14743017903,     7234.79425624200}, 
    {     0.00000000042,  3.43563949713,     5486.77784317500}, 
    {     0.00000000044,  4.47908248027,      426.59819087600}, 
    {     0.00000000040,  0.79167327114,        7.11354700080}, 
    {     0.00000000045,  6.24183361898,     2274.11694950980}, 
    {     0.00000000038,  1.09272124839,     9623.68827669120}, 
    {     0.00000000042,  4.60964038446,     6682.20517446780}, 
    {     0.00000000038,  6.18558685622,     5729.50644714900}, 
    {     0.00000000038,  4.61315601536,     7740.60678358880}, 
    {     0.00000000036,  3.14996505800,      639.89728631400}, 
    {     0.00000000040,  1.47221984696,    13365.97282514820}, 
    {     0.00000000034,  2.44888174358,     2288.34404351140}, 
    {     0.00000000033,  4.07561553526,     3532.06069281140}, 
    {     0.00000000033,  4.00337366796,      191.44826611160}, 
    {     0.00000000034,  2.61360044785,     4690.47983635860}, 
    {     0.00000000042,  2.12093492483,    12832.75874170460}, 
    {     0.00000000032,  4.50887364887,     7875.67186362420}, 
    {     0.00000000032,  1.57458654370,    10419.98628350760}, 
    {     0.00000000042,  4.64340929626,    15643.68020330980}, 
    {     0.00000000034,  5.06656541832,     6681.24210705180}, 
    {     0.00000000036,  0.28987292152,     3723.50895892300}, 
    {     0.00000000033,  4.52563219188,     4929.68532198360}, 
    {     0.00000000034,  2.74382990905,     6677.70173505060}, 
    {     0.00000000029,  4.82292532787,     6836.64525283380}, 
    {     0.00000000031,  1.25306031255,      242.72860397400}, 
    {     0.00000000040,  1.33261257095,     5331.35744374080}, 
    {     0.00000000034,  3.03578748114,     6681.20759974740}, 
    {     0.00000000028,  5.44161669691,    10021.85453375160}, 
    {     0.00000000028,  3.41041355991,    10021.82002644720}, 
    {     0.00000000029,  1.44701292203,    26724.89941359840}, 
    {     0.00000000027,  0.23446626513,     9830.38901398780}, 
    {     0.00000000031,  3.55930404825,     8969.56889691100}, 
    {     0.00000000027,  0.62554177429,     6681.29216370240}, 
    {     0.00000000028,  0.66108605606,     6283.07584999140}, 
    {     0.00000000026,  2.93963456706,     2544.31441988340}, 
    {     0.00000000028,  3.02947324104,     2281.23049651060}, 
    {     0.00000000026,  0.06758130889,    10818.13528691580}, 
    {     0.00000000033,  5.38463358374,      553.56940284240}, 
    {     0.00000000026,  1.18522107539,     8955.34180290940}, 
    {     0.00000000030,  5.72396134501,     3339.63210563160}, 
    {     0.00000000032,  2.01050754787,     5884.92684658320}, 
    {     0.00000000027,  3.74433763737,     6298.32832117640}, 
    {     0.00000000026,  1.03437538808,     6681.15754309680}, 
    {     0.00000000024,  0.07873299732,      382.89653222320}, 
    {     0.00000000027,  0.62459992026,     3553.91152213780}, 
    {     0.00000000024,  3.46652790647,     8031.09226305840}, 
    {     0.00000000027,  4.97242136909,     3767.21061757580}, 
    {     0.00000000021,  0.34500515713,      398.14900340820}, 
    {     0.00000000022,  0.16000431895,     6674.11130639880}, 
    {     0.00000000025,  4.80981908946,     7632.94325965020}, 
    {     0.00000000020,  1.03308861369,     7210.91581849420}, 
    {     0.00000000019,  1.00795666182,     7064.12138562280}, 
    {     0.00000000020,  5.08085454093,     6688.33840040040}, 
    {     0.00000000024,  4.53131373076,     1748.01641306700}, 
    {     0.00000000021,  1.00067762870,     6894.52394883760}, 
    {     0.00000000021,  2.68399619671,    10018.31416175040}, 
    {     0.00000000018,  0.24311256346,     3981.49003408200}, 
    {     0.00000000023,  3.25718834734,     5621.84292321040}, 
    {     0.00000000018,  5.22850479583,     3333.49887969900}, 
    {     0.00000000017,  0.65399461894,     3340.54511639700}, 
    {     0.00000000016,  2.23166601637,    10264.56588407340}, 
    {     0.00000000016,  3.99319122882,      951.71840625060}, 
    {     0.00000000017,  0.24322966235,     3340.67973700260}, 
    {     0.00000000015,  0.68756621158,     2699.73481931760}, 
    {     0.00000000015,  0.79676193982,     6438.49624942560}, 
    {     0.00000000019,  3.09984967041,     8273.82086703240}, 
    {     0.00000000018,  5.49826928276,     2146.16541647520}, 
    {     0.00000000014,  4.64772091449,     2118.76386037840}, 
    {     0.00000000015,  2.35470306373,     5092.15195811580}, 
    {     0.00000000014,  4.97209858575,    11081.21921028860}, 
    {     0.00000000017,  0.37871098191,    10575.40668294180}, 
    {     0.00000000014,  0.53224061765,     1066.49547719000}, 
    {     0.00000000014,  1.08680225227,     6040.34724601740}, 
    {     0.00000000015,  4.55907710983,     8270.29774868340}, 
    {     0.00000000016,  5.13375747116,     9468.26787725700}, 
    {     0.00000000013,  0.53705768941,     5088.62883976680}, 
    {     0.00000000013,  0.11088343011,      213.29909543800}, 
    {     0.00000000013,  1.73016080294,     8671.96987044060}, 
    {     0.00000000012,  3.99880295457,    13207.02930736500}, 
    {     0.00000000012,  4.09699657905,     6041.32756708560}, 
    {     0.00000000013,  5.63225993860,     3178.14579056760}, 
    {     0.00000000011,  3.61924209254,    11773.37681151540}, 
    {     0.00000000013,  4.97777304006,    10022.81760116760}, 
    {     0.00000000011,  2.29245339567,     2914.01423582380}, 
    {     0.00000000011,  0.17994697060,     9070.11887384880}, 
    {     0.00000000012,  5.15200495439,    10973.55568635000}, 
    {     0.00000000014,  6.05434498977,      640.87760738220}, 
    {     0.00000000011,  1.75779397460,     4562.46099302120}, 
    {     0.00000000012,  1.46467398653,    12964.30070339100}, 
    {     0.00000000010,  3.56966848964,    15113.98923821520}, 
    {     0.00000000009,  4.80839551981,     3325.35995551480}, 
    {     0.00000000010,  1.23311080707,     3360.96774609859}, 
    {     0.00000000009,  1.93544907019,    13760.59871020740}, 
    {     0.00000000010,  0.49076916855,     2810.92146160520}, 
    {     0.00000000010,  2.49016534434,    16173.37116840440}, 
    {     0.00000000009,  3.62373278148,     5614.72937620960}, 
    {     0.00000000009,  2.29700488106,     8429.24126646660}, 
    {     0.00000000009,  2.52785501283,     3427.92063123960}, 
    {     0.00000000009,  5.57605456632,     3355.86489788480}, 
    {     0.00000000008,  3.38386554244,     8827.39026987480}, 
    {     0.00000000008,  1.67431441943,    16706.58525184800}, 
    {     0.00000000008,  3.62389227844,    12310.18132361080}, 
    {     0.00000000008,  2.25791643317,      151.89728108520}, 
    {     0.00000000008,  3.08029498940,     6254.62666252360}, 
    {     0.00000000010,  2.86769411066,     3320.25710730100}, 
    {     0.00000000008,  3.03420706487,     1751.53953141600}, 
    {     0.00000000007,  0.11237624686,     3127.31333126180}, 
    {     0.00000000009,  4.92065236724,    11216.28429032400}, 
    {     0.00000000007,  3.67458682256,     3980.50971301380}, 
};


static const struct ln_vsop mars_radius_r4[RADIUS_R4] = {
    {     0.00000019551,  3.58210746512,     3340.61242669980}, 
    {     0.00000016322,  4.05115851142,     6681.22485339960}, 
    {     0.00000005848,  4.46381646580,    10021.83728009940}, 
    {     0.00000001533,  4.84332951095,    13362.44970679920}, 
    {     0.00000000375,  1.50951652931,     3185.19202726560}, 
    {     0.00000000340,  5.20519444932,    16703.06213349900}, 
    {     0.00000000152,  5.16376141170,     3344.13554504880}, 
    {     0.00000000126,  2.19183723061,     3496.03282613400}, 
    {     0.00000000148,  0.00000000000,        0.00000000000}, 
    {     0.00000000088,  0.10430359862,     3583.34103067380}, 
    {     0.00000000071,  5.56060980870,    20043.67456019880}, 
    {     0.00000000050,  5.56346631885,     6684.74797174860}, 
    {     0.00000000048,  2.91926298132,     2787.04302385740}, 
    {     0.00000000057,  1.86870004051,     6525.80445396540}, 
    {     0.00000000034,  3.63370917313,     3097.88382272579}, 
    {     0.00000000021,  2.30993179224,     1059.38193018920}, 
    {     0.00000000020,  4.04278354592,     4136.91043351620}, 
    {     0.00000000018,  4.17438755890,     3149.16416058820}, 
    {     0.00000000017,  5.90833786763,    23384.28698689860}, 
    {     0.00000000014,  1.98185426243,      155.42039943420}, 
    {     0.00000000013,  4.43167860883,     7477.52286021600}, 
    {     0.00000000017,  5.93839376025,    10025.36039844840}, 
    {     0.00000000015,  4.58867012625,     6489.77658728800}, 
    {     0.00000000014,  2.22119368504,     9866.41688066520}, 
    {     0.00000000013,  3.24667481494,     6127.65545055720}, 
    {     0.00000000013,  0.48623714297,     6923.95345737360}, 
    {     0.00000000012,  5.44223670746,     3738.76143010800}, 
    {     0.00000000016,  2.67418088918,     4399.99435688900}, 
    {     0.00000000014,  0.78383138857,     3894.18182954220}, 
    {     0.00000000011,  2.64507772215,     3341.59274776800}, 
    {     0.00000000012,  4.34268478367,     2388.89402044920}, 
    {     0.00000000012,  2.52802901788,     6836.64525283380}, 
    {     0.00000000009,  2.81895333303,     4292.33083295040}, 
    {     0.00000000012,  5.83109172622,     7079.37385680780}, 
    {     0.00000000009,  0.76993290644,     1592.59601363280}, 
    {     0.00000000008,  3.56780948809,      796.29800681640}, 
    {     0.00000000008,  2.59620253825,     4535.05943692440}, 
    {     0.00000000008,  3.91827119997,     6438.49624942560}, 
    {     0.00000000009,  2.21473599227,     1194.44701022460}, 
    {     0.00000000008,  1.21128945285,     4690.47983635860}, 
    {     0.00000000007,  3.08488687971,     2544.31441988340}, 
    {     0.00000000008,  5.72388554390,     1990.74501704100}, 
    {     0.00000000008,  3.00192257768,     3532.06069281140}, 
    {     0.00000000008,  4.44918099254,     3339.63210563160}, 
    {     0.00000000008,  3.21999751217,     3347.72597370060}, 
    {     0.00000000007,  1.16933312219,     4933.20844033260}, 
    {     0.00000000008,  5.12244052839,     3723.50895892300}, 
    {     0.00000000006,  4.60069136817,     5729.50644714900}, 
    {     0.00000000006,  1.82718202907,     2957.71589447660}, 
    {     0.00000000006,  3.00923601434,     6682.20517446780}, 
    {     0.00000000005,  2.74887623421,     1589.07289528380}, 
    {     0.00000000005,  2.01586492272,     5486.77784317500}, 
    {     0.00000000005,  6.17623487651,    13365.97282514820}, 
    {     0.00000000006,  3.96856230146,     2146.16541647520}, 
    {     0.00000000005,  2.80833888276,     3337.08930835080}, 
    {     0.00000000004,  2.92720462940,     7875.67186362420}, 
    {     0.00000000004,  4.02001405595,     3333.49887969900}, 
};


static const struct ln_vsop mars_radius_r5[RADIUS_R5] = {
    {     0.00000000475,  2.47621038205,     6681.22485339960}, 
    {     0.00000000270,  2.90961348988,    10021.83728009940}, 
    {     0.00000000116,  1.76766655427,     3340.61242669980}, 
    {     0.00000000097,  3.31315004582,    13362.44970679920}, 
    {     0.00000000049,  6.28284800757,     3185.19202726560}, 
    {     0.00000000027,  3.69297278191,    16703.06213349900}, 
    {     0.00000000013,  3.67011956659,     3496.03282613400}, 
    {     0.00000000012,  4.88179002689,     3583.34103067380}, 
    {     0.00000000012,  3.14159265359,        0.00000000000}, 
    {     0.00000000009,  4.05335755845,    20043.67456019880}, 
    {     0.00000000009,  0.35575801457,     6525.80445396540}, 
    {     0.00000000006,  3.95186839136,     6684.74797174860}, 
    {     0.00000000005,  1.40424074649,     2787.04302385740}, 
    {     0.00000000005,  3.60327227648,     3344.13554504880}, 
    {     0.00000000004,  5.11981331029,     3097.88382272579}, 
    {     0.00000000004,  5.24603068590,     6923.95345737360}, 
    {     0.00000000002,  0.40954426011,     9866.41688066520}, 
};

/*! \fn void ln_get_mars_equ_coords (double JD, struct ln_equ_posn * position);
* \param JD julian Day
* \param position Pointer to store position
*
* Calculates Mars equatorial position for given julian day.
* This function includes calculations for planetary aberration and refers
* to the FK5 reference frame.
*
* To get the complete equatorial coordinates, corrections for nutation
* have to be applied.
*
* The position returned is accurate to within 0.1 arcsecs.
*/ 
void ln_get_mars_equ_coords (double JD, struct ln_equ_posn * position)
{
	struct ln_helio_posn h_sol, h_mars;
	struct ln_rect_posn g_sol, g_mars;
	double a,b,c;
	double ra, dec, delta, diff, last, t = 0;
	
	/* need typdef for solar heliocentric coords */
	ln_get_solar_geom_coords (JD, &h_sol);
	ln_get_rect_from_helio (&h_sol, &g_sol);
	
	do {
		last = t;
		ln_get_mars_helio_coords (JD - t, &h_mars);
		ln_get_rect_from_helio (&h_mars, &g_mars);

		/* equ 33.10 pg 229 */
		a = g_sol.X + g_mars.X;
		b = g_sol.Y + g_mars.Y;
		c = g_sol.Z + g_mars.Z;
	
		delta = a*a + b*b + c*c;
		delta = sqrt (delta);
		t = delta * 0.0057755183;
		diff = t - last;
	} while (diff > 0.0001 || diff < -0.0001);
		
	ra = atan2 (b,a);
	dec = c / delta;
	dec = asin (dec);

	/* back to hours, degrees */
	position->ra = ln_range_degrees(ln_rad_to_deg (ra));
	position->dec = ln_rad_to_deg (dec);
}
	

/*! \fn void ln_get_mars_helio_coords (double JD, struct ln_helio_posn * position)
* \param JD Julian Day
* \param position Pointer to store heliocentric position
*
* Calculate Mars heliocentric (refered to the centre of the Sun) coordinates
* in the FK5 reference frame for the given julian day.
* Longitude and Latitude are in degrees, whilst radius vector is in AU.
*/
/* Chapter 31 Pg 206-207 Equ 31.1 31.2 , 31.3 using VSOP 87 
*/
void ln_get_mars_helio_coords (double JD, struct ln_helio_posn * position)
{
	double t, t2, t3, t4, t5;
	double L0, L1, L2, L3, L4, L5;
	double B0, B1, B2, B3, B4, B5;
	double R0, R1, R2, R3, R4, R5;
	
	/* check cache first */
	if (JD == cJD) {
		/* cache hit */
		position->L = cL;
		position->B = cB;
		position->R = cR;
		return;
	}
	
	/* get julian ephemeris day */
	t = (JD - 2451545.0) / 365250;
	t2 = t * t;
	t3 = t2 * t;
	t4 = t3 * t;
	t5 = t4 * t;
	
	/* calc L series */
	L0 = ln_calc_series (mars_longitude_l0, LONG_L0, t);
	L1 = ln_calc_series (mars_longitude_l1, LONG_L1, t);
	L2 = ln_calc_series (mars_longitude_l2, LONG_L2, t);
	L3 = ln_calc_series (mars_longitude_l3, LONG_L3, t);
	L4 = ln_calc_series (mars_longitude_l4, LONG_L4, t);
	L5 = ln_calc_series (mars_longitude_l5, LONG_L5, t);
	position->L = (L0 + L1 * t + L2 * t2 + L3 * t3 + L4 * t4 + L5 * t5);

	/* calc B series */
	B0 = ln_calc_series (mars_latitude_b0, LAT_B0, t);
	B1 = ln_calc_series (mars_latitude_b1, LAT_B1, t);
	B2 = ln_calc_series (mars_latitude_b2, LAT_B2, t);
	B3 = ln_calc_series (mars_latitude_b3, LAT_B3, t);
	B4 = ln_calc_series (mars_latitude_b4, LAT_B4, t);
	B5 = ln_calc_series (mars_latitude_b5, LAT_B5, t);
	position->B = (B0 + B1 * t + B2 * t2 + B3 * t3 + B4 * t4 + B5 * t5);


	/* calc R series */
	R0 = ln_calc_series (mars_radius_r0, RADIUS_R0, t);
	R1 = ln_calc_series (mars_radius_r1, RADIUS_R1, t);
	R2 = ln_calc_series (mars_radius_r2, RADIUS_R2, t);
	R3 = ln_calc_series (mars_radius_r3, RADIUS_R3, t);
	R4 = ln_calc_series (mars_radius_r4, RADIUS_R4, t);
	R5 = ln_calc_series (mars_radius_r5, RADIUS_R5, t);
	position->R = (R0 + R1 * t + R2 * t2 + R3 * t3 + R4 * t4 + R5 * t5);
	
	/* change to degrees in correct quadrant */
	position->L = ln_rad_to_deg(position->L);
	position->B = ln_rad_to_deg(position->B);
	position->L = ln_range_degrees(position->L);
	
	/* change to fk5 reference frame */
	ln_vsop87_to_fk5 (position, JD);
	
	/* save cache */
	cJD = JD;
	cL = position->L;
	cB = position->B;
	cR = position->R;
}

/*! \fn double ln_get_mars_earth_dist (double JD);
* \brief Calculate the distance between Mars and the Earth in AU.
* \param JD Julian Day
* \return Distance in AU
*
* Calculates the distance in AU between the Earth and Mars for the given 
* julian day.
*/
double ln_get_mars_earth_dist (double JD)
{
	struct ln_helio_posn h_mars, h_earth;
	struct ln_rect_posn g_mars, g_earth;
	double x, y, z;
	
	/* get heliocentric positions */
	ln_get_mars_helio_coords (JD, &h_mars);
	ln_get_earth_helio_coords (JD, &h_earth);
	
	/* get geocentric coords */
	ln_get_rect_from_helio (&h_mars, &g_mars);
	ln_get_rect_from_helio (&h_earth, &g_earth);
	
	/* use pythag */
	x = g_mars.X - g_earth.X;
	y = g_mars.Y - g_earth.Y;
	z = g_mars.Z - g_earth.Z;
	x = x * x;
	y = y * y;
	z = z * z;

	return sqrt (x + y + z);
}
	
/*! \fn double ln_get_mars_solar_dist (double JD);
* \brief Calculate the distance between Mars and the Sun in AU
* \param JD Julian Day.
* \return Distance in AU.
*
* Calculates the distance in AU between the Sun and Mars for the given 
* julian day.
*/ 
double ln_get_mars_solar_dist (double JD)
{
	struct ln_helio_posn h_mars;

	/* get heliocentric position */
	ln_get_mars_helio_coords (JD, &h_mars);
	
	return h_mars.R;
}
	
/*! \fn double ln_get_mars_magnitude (double JD);
* \brief Calculate the visible magnitude of Mars
* \param JD Julian Day
* \return Magnitude of Mars
*
* Calculate the visisble magnitude of Mars for given julian day.
*/ 
double ln_get_mars_magnitude (double JD)
{
	double delta, r, i;
	
	/* get distances */
	r = ln_get_mars_solar_dist (JD);
	delta = ln_get_mars_earth_dist (JD);
	
	/* get phase */
	i = ln_get_mars_phase (JD);
	
	return -1.52 + 5 * log10 (r * delta) + 0.016 * i;
}

/*! \fn double ln_get_mars_disk (double JD);
* \brief Calculate the illuminated fraction of Mars disk
* \param JD Julian Day.
* \return Illuminated fraction of Mars disk (Value between 0 - 1)
*
* Calculates the illuminated fraction of Mars disk for given julian day.
*/ 
/* Chapter 41 */
double ln_get_mars_disk (double JD)
{
	double r,delta,R;	
	
	/* get distances */
	R = ln_get_earth_solar_dist (JD);
	r = ln_get_mars_solar_dist (JD);
	delta = ln_get_mars_earth_dist (JD);
	
	/* calc fraction angle */
	return (((r + delta) * (r + delta)) - R * R) / (4 * r * delta);
	
}

/*! \fn double ln_get_mars_phase (double JD);
* \brief Calculate the phase angle of Mars (Sun - Mars - Earth)
* \param JD Julian Day
* \return Phase angle of Mars (degrees)
*
* Calculates the phase angle of Mars for the given julian day.
*/ 
/* Chapter 41 */
double ln_get_mars_phase (double JD)
{
	double i,r,delta,R;	
	
	/* get distances */
	R = ln_get_earth_solar_dist (JD);
	r = ln_get_mars_solar_dist (JD);
	delta = ln_get_mars_earth_dist (JD);

	/* calc phase */
	i = (r * r + delta * delta - R * R) / (2 * r * delta);
	i = acos (i);
	return ln_rad_to_deg (i);
}


/*! \fn double ln_get_mars_rst (double JD, struct ln_lnlat_posn * observer, struct ln_rst_time * rst);
* \param JD Julian day
* \param observer Observers position
* \param rst Pointer to store Rise, Set and Transit time in JD
* \return 0 for success, else 1 for circumpolar.
*
* Calculate the time the rise, set and transit (crosses the local meridian at upper culmination)
* time of Mars for the given Julian day.
*
* Note: this functions returns 1 if Mars is circumpolar, that is it remains the whole
* day either above or below the horizon.
*/
int ln_get_mars_rst (double JD, struct ln_lnlat_posn * observer, struct ln_rst_time * rst)
{
	return ln_get_body_rst_horizon (JD, observer, ln_get_mars_equ_coords, LN_STAR_STANDART_HORIZON, rst);
}


/*! \fn double ln_get_mars_sdiam (double JD)
* \param JD Julian day
* \return Semidiameter in arc seconds
*
* Calculate the semidiameter of Mars in arc seconds for the 
* given julian day.
*/
double ln_get_mars_sdiam (double JD)
{
	double So = 4.68; /* at 1 AU */
	double dist;
	
	dist = ln_get_mars_earth_dist (JD);
	return So / dist;
}
	
/*! \fn void ln_get_mars_rect_helio (double JD, struct ln_rect_posn * position)
* \param JD Julian day.
* \param position ointer to return position
*
* Calculate Mars rectangular heliocentric coordinates for the
* given Julian day. Coordinates are in AU.
*/
void ln_get_mars_rect_helio (double JD, struct ln_rect_posn * position)
{
	struct ln_helio_posn mars;
		
	ln_get_mars_helio_coords (JD, &mars);
	ln_get_rect_from_helio (&mars, position);
}

/*! \example mars.c
 * 
 * Examples of how to use planetary functions. 
 */
